Solved: In 117-126, expressions that occur in calculus are given. Faclor completely each

The numbers in the set {x x = b' where a, b are integers and b *' O}, are called ____ numbers.

The value of the expression 4 + 56 - 3 is ____ _

The ____ fact that 2x + 3x = (2 + 3)x is a consequence of the Property.

"The product of 5 and x + 3 equals 6" may be written as ____.

True or False Rational numbers have decimals that either terminate or are non terminating with a repeating block of digits.

True or False The Zero-Product Property states that the product of any number and zero equals zero.

True or False The least common multiple of 12 and 18 is 6.

True or False No real number is both rational and irrational.

In Problems 9-20, use U = universal set = {O, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {I, 3, 4, 5, 9}, B = {2, 4, 6, 7, 8}, and e = {I, 3, 4, 6} to find each set. AUB

In Problems 9-20, use U = universal set = {O, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {I, 3, 4, 5, 9}, B = {2, 4, 6, 7, 8}, and e = {I, 3, 4, 6} to find each set. A ue

In Problems 9-20, use U = universal set = {O, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {I, 3, 4, 5, 9}, B = {2, 4, 6, 7, 8}, and e = {I, 3, 4, 6} to find each set. An B

In Problems 9-20, use U = universal set = {O, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {I, 3, 4, 5, 9}, B = {2, 4, 6, 7, 8}, and e = {I, 3, 4, 6} to find each set. Ane

In Problems 9-20, use U = universal set = {O, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {I, 3, 4, 5, 9}, B = {2, 4, 6, 7, 8}, and e = {I, 3, 4, 6} to find each set. (A U B)ne

In Problems 9-20, use U = universal set = {O, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {I, 3, 4, 5, 9}, B = {2, 4, 6, 7, 8}, and e = {I, 3, 4, 6} to find each set. ( A n B)Ue

In Problems 9-20, use U = universal set = {O, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {I, 3, 4, 5, 9}, B = {2, 4, 6, 7, 8}, and e = {I, 3, 4, 6} to find each set. A

In Problems 9-20, use U = universal set = {O, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {I, 3, 4, 5, 9}, B = {2, 4, 6, 7, 8}, and e = {I, 3, 4, 6} to find each set. e

In Problems 9-20, use U = universal set = {O, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {I, 3, 4, 5, 9}, B = {2, 4, 6, 7, 8}, and e = {I, 3, 4, 6} to find each set. An B

In Problems 9-20, use U = universal set = {O, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {I, 3, 4, 5, 9}, B = {2, 4, 6, 7, 8}, and e = {I, 3, 4, 6} to find each set. Bue AUB

In Problems 9-20, use U = universal set = {O, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {I, 3, 4, 5, 9}, B = {2, 4, 6, 7, 8}, and e = {I, 3, 4, 6} to find each set.

In Problems 9-20, use U = universal set = {O, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {I, 3, 4, 5, 9}, B = {2, 4, 6, 7, 8}, and e = {I, 3, 4, 6} to find each set. Bne

In Problems 21-26, list the numbers in each set that are (a) Natural numbers, (b) Integers, (c) Rational numbers, (d) Irrational numbers, (e) Real numbers. A - -6 ' 2 , -1 .333 ... (the 3 s repeat), ?T, 2,5

In Problems 21-26, list the numbers in each set that are (a) Natural numbers, (b) Integers, (c) Rational numbers, (d) Irrational numbers, (e) Real numbers. B = { - , 2.060606 ... (the block 06 repeats), 1 .25, 0, 1, Vs }

In Problems 21-26, list the numbers in each set that are (a) Natural numbers, (b) Integers, (c) Rational numbers, (d) Irrational numbers, (e) Real numbers. C = 0, 1, 2' 3' 4 }

In Problems 21-26, list the numbers in each set that are (a) Natural numbers, (b) Integers, (c) Rational numbers, (d) Irrational numbers, (e) Real numbers. D = {-I, -1.1, - 1.2, -1.3}

In Problems 21-26, list the numbers in each set that are (a) Natural numbers, (b) Integers, (c) Rational numbers, (d) Irrational numbers, (e) Real numbers. E = { \12, ?T, \12 + 1, ?T + }

In Problems 21-26, list the numbers in each set that are (a) Natural numbers, (b) Integers, (c) Rational numbers, (d) Irrational numbers, (e) Real numbers. F = { - \I2' ?T + \12, + 10.3 }

In Problems 2 7-38, approximate each number (a) rounded and (b) truncated to three decimal places. 1 8.9526

In Problems 2 7-38, approximate each number (a) rounded and (b) truncated to three decimal places. 25.86134

In Problems 2 7-38, approximate each number (a) rounded and (b) truncated to three decimal places. 28.65319

In Problems 2 7-38, approximate each number (a) rounded and (b) truncated to three decimal places. 99.05249

In Problems 2 7-38, approximate each number (a) rounded and (b) truncated to three decimal places. 0.06291

In Problems 2 7-38, approximate each number (a) rounded and (b) truncated to three decimal places. 0.05388

In Problems 2 7-38, approximate each number (a) rounded and (b) truncated to three decimal places. 9.9985

In Problems 2 7-38, approximate each number (a) rounded and (b) truncated to three decimal places. 1 .0006

In Problems 2 7-38, approximate each number (a) rounded and (b) truncated to three decimal places. 3 35. "

In Problems 2 7-38, approximate each number (a) rounded and (b) truncated to three decimal places. 5 36. "

In Problems 2 7-38, approximate each number (a) rounded and (b) truncated to three decimal places. 521 15

In Problems 2 7-38, approximate each number (a) rounded and (b) truncated to three decimal places. 8 5 1

In Problems 39-48, write each statement using symbols. The sum of 3 and 2 equals 5.

In Problems 39-48, write each statement using symbols. The product of 5 and 2 equals 10.

In Problems 39-48, write each statement using symbols. The sum of x and 2 is the product of 3 and 4.

In Problems 39-48, write each statement using symbols. The sum of 3 and y is the sum of 2 and 2

In Problems 39-48, write each statement using symbols. The product of 3 and y is the sum of 1 and 2.

In Problems 39-48, write each statement using symbols. The product of 2 and x is the product of 4 and 6.

In Problems 39-48, write each statement using symbols. The difference x less 2 equals 6.

In Problems 39-48, write each statement using symbols. The difference 2 less y equals 6.

In Problems 39-48, write each statement using symbols. The quotient x divided by 2 is 6.

In Problems 39-48, write each statement using symbols. The quotient 2 divided by x is 6.

In Problems 49-86, evaluate each expression. 9 - 4 + 2

In Problems 49-86, evaluate each expression. 6 - 4 + 3

In Problems 49-86, evaluate each expression. -6 + 43

In Problems 49-86, evaluate each expression. 8 - 42

In Problems 49-86, evaluate each expression. 4 + 5 - 8

In Problems 49-86, evaluate each expression. 8 - 3 - 4

In Problems 49-86, evaluate each expression. 4 + 3

In Problems 49-86, evaluate each expression. 2 - 2

In Problems 49-86, evaluate each expression. 6 - [3 '5 + 2'(3 - 2)]

In Problems 49-86, evaluate each expression. 2 [8 - 3 (4 + 2)] - 3

In Problems 49-86, evaluate each expression. 2 (3 - 5) + 8 2 - 1

In Problems 49-86, evaluate each expression. 1 - (4 ' 3 - 2 + 2)

In Problems 49-86, evaluate each expression. 10 - [6 - 22 + (8 - 3) J 2

In Problems 49-86, evaluate each expression. 2 - 5 4 - [6 (3 - 4) J

In Problems 49-86, evaluate each expression. (5 - 3)2

In Problems 49-86, evaluate each expression. (5 + 4) 3

In Problems 49-86, evaluate each expression. 4 + 8 5 - 3

In Problems 49-86, evaluate each expression. 2 - 4 5 - 3

In Problems 49-86, evaluate each expression. 3 10 5' 21

In Problems 49-86, evaluate each expression. 5 3 -.-9 10

In Problems 49-86, evaluate each expression. . 10 25 27

In Problems 49-86, evaluate each expression. 21 . 100 25 3

In Problems 49-86, evaluate each expression. 3 2 4 + 5

In Problems 49-86, evaluate each expression. 4 1 - + - 3 2

In Problems 49-86, evaluate each expression. 5 9 (5 + 5

In Problems 49-86, evaluate each expression. 8 15 - + - 9 2

In Problems 49-86, evaluate each expression. 5 1 - + - 18 12

In Problems 49-86, evaluate each expression. 2 8 - + - 15 9

In Problems 49-86, evaluate each expression. 1 7 - - - 30 18

In Problems 49-86, evaluate each expression. 3 2 - - - 14 21

In Problems 49-86, evaluate each expression. 3 2 - - - 20 15

In Problems 49-86, evaluate each expression. 6 3 - - - 35 14

In Problems 49-86, evaluate each expression. 5 18 11 27

In Problems 49-86, evaluate each expression. 5 2 35

In Problems 49-86, evaluate each expression. 1 3 7 -.- + - 2 5 10

In Problems 49-86, evaluate each expression. 2 4 1 -+- ' - 3 5 6

In Problems 49-86, evaluate each expression. 3 3 2- + - 4 8

In Problems 49-86, evaluate each expression. 5 1 3- - - 6 2

In Problems 87-98, use the Distributive Property to remove the parentheses. 6(x + 4)

In Problems 87-98, use the Distributive Property to remove the parentheses. 4(2x - 1)

In Problems 87-98, use the Distributive Property to remove the parentheses. x(x - 4)

In Problems 87-98, use the Distributive Property to remove the parentheses. 4x(x + 3)

In Problems 87-98, use the Distributive Property to remove the parentheses. 2(r - 1:.) 4 2

In Problems 87-98, use the Distributive Property to remove the parentheses. 3(X + 1:.) 3 6

In Problems 87-98, use the Distributive Property to remove the parentheses. (x + 2) (x + 4)

In Problems 87-98, use the Distributive Property to remove the parentheses. (x + 5)(x + 1)

In Problems 87-98, use the Distributive Property to remove the parentheses. (x - 2)(x + 1)

In Problems 87-98, use the Distributive Property to remove the parentheses. (x - 4)(x + 1)

In Problems 87-98, use the Distributive Property to remove the parentheses. (x - 8)(x - 2)

In Problems 87-98, use the Distributive Property to remove the parentheses. (x - 4)(x - 2)

Explain to a friend how the D istributive Property is used to justify the fact that 2x + 3x = 5x.

Explain to a friend why 2 + 3 4 = 14, whereas (2 + 3) ' 4 = 20.

Explain why 2(3 . 4) is not equal to (2 3) . (2 ' 4).

Explam why 2 + 5 IS not equal to 2 + "5'

Is subtraction commutative? Support your conclusion with an example.

Is subtraction associative? Support your conclusion with an example.

Is division commutative? Support your conclusion with an example.

Is division associative? Support your conclusion with an example.

If 2 = x, why does x = 2?

If x = 5, why does x2 + x = 30?

Are there any real numbers that are both rational and irrational? Are there any real numbers that are neither? Explain your reasoning.

Explain why the sum of a rational number and an irrational number must be irrational.

A rational number is defined as the quotient of two integers. When written as a decimal, the decimal will either repeat or terminate. By looking at the denominator of the rational number, there is a way to tell in advance whether its decimal representation will repeat or terminate. Make a list of rational numbers and their decimals. See if you can discover the pattern. Confirm your conclusion by consulting books on number theory at the library. Write a brief essay on your findings.

The current time is 12 noon CST. What time (CST) will it be 12,997 hours from now?

Both 0 a "* 0 and 0 are undefmed, but for dIfferent reasons. Write a paragraph or two explaining the different reasons.

A(n) is a letter used in algebra to represent any number from a given set of numbers.

On the real number line, the real number zero is the coordinate of the ___ _

An inequality of the form a > b is called a(n) ___ _ inequality.

In the expression 2\ the number 2 is called the ___ _ and 4 is called the ___ _

In scientific notation, 1234.5678 = ___ _

True or False The product of two negative real numbers is always greater than zero.

True or False The distance between two distinct points on the real number line is always greater than zero.

True or False The absolute value of a real number is always greater than zero.

True or False When a number is expressed in scientific notation, it is expressed as the product of a number x, 0 :s x < 1, and a power of 10.

True or False To multiply two expressions having the same base, retain the base and multiply the exponents.

On the real number line, label the points with coordinates 0, 1, -1, , -2.5, , and 0.25. 2 4

Repeat Problem 11 for the coordinates 0, -2,2, -1.5, ,, and

In Problems 13-22, replace the question mark by <, >, or =, whichever is correct. ?0

In Problems 13-22, replace the question mark by <, >, or =, whichever is correct. 5 ? 6

In Problems 13-22, replace the question mark by <, >, or =, whichever is correct. -1 ? -2

In Problems 13-22, replace the question mark by <, >, or =, whichever is correct. -3 ?. - - 2

In Problems 13-22, replace the question mark by <, >, or =, whichever is correct.

In Problems 13-22, replace the question mark by <, >, or =, whichever is correct. v2? 1.41

In Problems 13-22, replace the question mark by <, >, or =, whichever is correct. ? 0.5

In Problems 13-22, replace the question mark by <, >, or =, whichever is correct. ? 0.33

In Problems 13-22, replace the question mark by <, >, or =, whichever is correct. 2 "3? .0. 6 7

In Problems 13-22, replace the question mark by <, >, or =, whichever is correct. ? 0.25

In Problems 23-28, write each statement as an inequality. x is positive

In Problems 23-28, write each statement as an inequality. z is negative

In Problems 23-28, write each statement as an inequality. x is less than 2

In Problems 23-28, write each statement as an inequality. Y is greater than -5

In Problems 23-28, write each statement as an inequality. x is less than or equal to 1

In Problems 23-28, write each statement as an inequality. x is greater than or equal to 2

In Problems 29-32, graph the numbers x on the real number line. x -2

In Problems 29-32, graph the numbers x on the real number line. x < 4

In Problems 29-32, graph the numbers x on the real number line. x> -1

In Problems 29-32, graph the numbers x on the real number line. x:=:;7

In Problems 33-38, use the given real number line to compute each distance. A BCD E -4 -3 -2 -1 0 2 3 4 5 6 d(C, D)

In Problems 33-38, use the given real number line to compute each distance. A BCD E -4 -3 -2 -1 0 2 3 4 5 7 d(C, A)

In Problems 33-38, use the given real number line to compute each distance. A BCD E -4 -3 -2 -1 0 2 3 4 5 8 d(D,E)

In Problems 33-38, use the given real number line to compute each distance. A BCD E -4 -3 -2 -1 0 2 3 4 5 9 d(C, E)

In Problems 33-38, use the given real number line to compute each distance. A BCD E -4 -3 -2 -1 0 2 3 4 5 10 d(A, E)

In Problems 33-38, use the given real number line to compute each distance. A BCD E -4 -3 -2 -1 0 2 3 4 5 11 d(D, B)

In Problems 39-46, evaluate each expression if x = -2 and y = 3. x + 2y

In Problems 39-46, evaluate each expression if x = -2 and y = 3. 3x + y

In Problems 39-46, evaluate each expression if x = -2 and y = 3. 5xy + 2

In Problems 39-46, evaluate each expression if x = -2 and y = 3. -2x + xy

In Problems 39-46, evaluate each expression if x = -2 and y = 3. 2x -x-y

In Problems 39-46, evaluate each expression if x = -2 and y = 3. x+y -x-y

In Problems 39-46, evaluate each expression if x = -2 and y = 3. 3x + 2y --- 2 +

In Problems 39-46, evaluate each expression if x = -2 and y = 3. 2x - 3 --Y

In Problems 47-56, find the value of each expression if x = 3 and y = -2. x + y

In Problems 47-56, find the value of each expression if x = 3 and y = -2. x - yl

In Problems 47-56, find the value of each expression if x = 3 and y = -2. xl + Iy

In Problems 47-56, find the value of each expression if x = 3 and y = -2. xl -Iyl

In Problems 47-56, find the value of each expression if x = 3 and y = -2. xl -x

In Problems 47-56, find the value of each expression if x = 3 and y = -2. hl y

In Problems 47-56, find the value of each expression if x = 3 and y = -2. 4x - 5yl

In Problems 47-56, find the value of each expression if x = 3 and y = -2. 3x + 2yl

In Problems 47-56, find the value of each expression if x = 3 and y = -2. 11 4xl -15yll

In Problems 47-56, find the value of each expression if x = 3 and y = -2. 3 1 xl + 21yl

In Problems 57-64, determine which of the valuers) (a) through (d), if any, must be excluded from the domain of the variable in each expression: (a) x = 3 (b)x=1 (c)x=O (d) x = -1 x2 -1 -x

In Problems 57-64, determine which of the valuers) (a) through (d), if any, must be excluded from the domain of the variable in each expression: (a) x = 3 (b)x=1 (c)x=O (d) x = -1 x2 + 1 --x

In Problems 57-64, determine which of the valuers) (a) through (d), if any, must be excluded from the domain of the variable in each expression: (a) x = 3 (b)x=1 (c)x=O (d) x = -1 x -- x -9

In Problems 57-64, determine which of the valuers) (a) through (d), if any, must be excluded from the domain of the variable in each expression: (a) x = 3 (b)x=1 (c)x=O (d) x = -1 x -1-x-+ 9

In Problems 57-64, determine which of the valuers) (a) through (d), if any, must be excluded from the domain of the variable in each expression: (a) x = 3 (b)x=1 (c)x=O (d) x = -1 x2 -- x2 + I

In Problems 57-64, determine which of the valuers) (a) through (d), if any, must be excluded from the domain of the variable in each expression: (a) x = 3 (b)x=1 (c)x=O (d) x = -1 x3 -- x -I

In Problems 57-64, determine which of the valuers) (a) through (d), if any, must be excluded from the domain of the variable in each expression: (a) x = 3 (b)x=1 (c)x=O (d) x = -1 x2 + 5x -10 ----- x3 -x

In Problems 57-64, determine which of the valuers) (a) through (d), if any, must be excluded from the domain of the variable in each expression: (a) x = 3 (b)x=1 (c)x=O (d) x = -1 -9x2 -X + 1 ---:;--- x + x

In Problems 65-68, determine the domain of the variable x in each expression. 4 -x-5

In Problems 65-68, determine the domain of the variable x in each expression. x+4

In Problems 65-68, determine the domain of the variable x in each expression. x -x+4

In Problems 65-68, determine the domain of the variable x in each expression. X -? -- x -6

In Problems 69-72, use the formula C = % (F - 3 2) for converting degrees Fahrenheit into degrees Celsius to find the Celsius measure of each Fahrenheit temperature. F = 3 2

In Problems 69-72, use the formula C = % (F - 3 2) for converting degrees Fahrenheit into degrees Celsius to find the Celsius measure of each Fahrenheit temperature. F = 212

In Problems 69-72, use the formula C = % (F - 3 2) for converting degrees Fahrenheit into degrees Celsius to find the Celsius measure of each Fahrenheit temperature. F = 77

In Problems 69-72, use the formula C = % (F - 3 2) for converting degrees Fahrenheit into degrees Celsius to find the Celsius measure of each Fahrenheit temperature. F = -4

In Problems 73-84, simplify each expression. (-4?

In Problems 73-84, simplify each expression. -42

In Problems 73-84, simplify each expression. 4 - 2

In Problems 73-84, simplify each expression. -4-2

In Problems 73-84, simplify each expression. 36 34

In Problems 73-84, simplify each expression. 4-2 3

In Problems 73-84, simplify each expression. 3-2-1

In Problems 73-84, simplify each expression. 2-1-3

In Problems 73-84, simplify each expression. v25

In Problems 73-84, simplify each expression. V36

In Problems 73-84, simplify each expression. 42

In Problems 73-84, simplify each expression. -32

In Problems 85-94, simplify each expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not O. (8x3)2

In Problems 85-94, simplify each expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not O. (-4x2rl

In Problems 85-94, simplify each expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not O. (x2 y-1 2)

In Problems 85-94, simplify each expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not O. (x-1 y3)

In Problems 85-94, simplify each expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not O. x2l--4xy

In Problems 85-94, simplify each expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not O.

In Problems 85-94, simplify each expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not O.

In Problems 85-94, simplify each expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not O.

In Problems 85-94, simplify each expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not O. (3X-1 )- 2

In Problems 85-94, simplify each expression. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not O. (5[2 )- 3 6y- 2

In Problems 95-106, find the value of each expression if x = 2 and y = -l. 2xyl

In Problems 95-106, find the value of each expression if x = 2 and y = -l. -3[1 Y

In Problems 95-106, find the value of each expression if x = 2 and y = -l. x2 + l

In Problems 95-106, find the value of each expression if x = 2 and y = -l. x2y2

In Problems 95-106, find the value of each expression if x = 2 and y = -l. (xy)2

In Problems 95-106, find the value of each expression if x = 2 and y = -l. (x + y?

In Problems 95-106, find the value of each expression if x = 2 and y = -l. 0

In Problems 95-106, find the value of each expression if x = 2 and y = -l. x2

In Problems 95-106, find the value of each expression if x = 2 and y = -l. yx2 + l

In Problems 95-106, find the value of each expression if x = 2 and y = -l. #+V

In Problems 95-106, find the value of each expression if x = 2 and y = -l. xl'

In Problems 95-106, find the value of each expression if x = 2 and y = -l. yt

Find the value of the expression 2x3 - 3x2 + 5x - 4 if x = 2. What is the value if x = I?

Find the value of the expression 4x3 + 3x2 - X + 2 if x = 1. What is the value if x = 2?

What is the value of --4 ? (222

What is the value of (0.1 )3(20)3?

In Problems 111-118, use a calculator to evaluate each expression. Round your answer to three decimal places. (8.2)6

In Problems 111-118, use a calculator to evaluate each expression. Round your answer to three decimal places. (3.7)5

In Problems 111-118, use a calculator to evaluate each expression. Round your answer to three decimal places. (6.1)-3

In Problems 111-118, use a calculator to evaluate each expression. Round your answer to three decimal places. (2.2f5

In Problems 111-118, use a calculator to evaluate each expression. Round your answer to three decimal places. (-2.8)6

In Problems 111-118, use a calculator to evaluate each expression. Round your answer to three decimal places. -(2.8)6

In Problems 111-118, use a calculator to evaluate each expression. Round your answer to three decimal places. (-8.11f4

In Problems 111-118, use a calculator to evaluate each expression. Round your answer to three decimal places. -(8.11f4

In Problems 119-126, write each number in scientific notation. 454.2

In Problems 119-126, write each number in scientific notation. 32.14

In Problems 119-126, write each number in scientific notation. 0.013

In Problems 119-126, write each number in scientific notation. 0.00421

In Problems 119-126, write each number in scientific notation. 32,155

In Problems 119-126, write each number in scientific notation. 21,210

In Problems 119-126, write each number in scientific notation. 0.000423

In Problems 119-126, write each number in scientific notation. 0.0514

In Problems 127-134, write each number as a decimal. 6.15 x 104

In Problems 127-134, write each number as a decimal. 9.7 x 103

In Problems 127-134, write each number as a decimal. 1.214 x 10-3

In Problems 127-134, write each number as a decimal. 9.88 X 10-4

In Problems 127-134, write each number as a decimal. 1.1 X 108

In Problems 127-134, write each number as a decimal. 4.112 x 102

In Problems 127-134, write each number as a decimal. 8.1 x 10-2

In Problems 127-134, write each number as a decimal. 6.453 x 10-1

In Problems 135-144, express each statement as an equation involving the indicated variables. Area of a Rectangle The area A of a rectangle is the product of its length I and its width w.

In Problems 135-144, express each statement as an equation involving the indicated variables. Perimeter of a Rectangle The perimeter P of a rectangle is twice the sum of its length I and its width w.

In Problems 135-144, express each statement as an equation involving the indicated variables. Circllmference of a Circle The circumference C of a circle is the product of 7T and its diameter d. g

In Problems 135-144, express each statement as an equation involving the indicated variables. Area of a Triangle The area A of a triangle is one-half the product of its base b and its height h. b

In Problems 135-144, express each statement as an equation involving the indicated variables. Area of an Equilateral Triangle The area A of an equilateral triangle is -times the square of the length x of one side. 4

In Problems 135-144, express each statement as an equation involving the indicated variables. Perimeter of an Equilateral Triangle The perimeter P of an equilateral triangle is 3 times the length x of one side.

In Problems 135-144, express each statement as an equation involving the indicated variables. Volume of a Sphere The volume V of a sphere is times 7T times the cube of the radius r. 3

In Problems 135-144, express each statement as an equation involving the indicated variables. Surface Area of a Sphere The surface area S of a sphere is 4 times 7T times the square of the radius r.

In Problems 135-144, express each statement as an equation involving the indicated variables. Volume of a Cube The volume V of a cube is the cube of the length x of a side. ' x

In Problems 135-144, express each statement as an equation involving the indicated variables. Surface Area of a Cube The surface area S of a cube is 6 times the square of the length x of a side.

Manufacturing Cost The weekly production cost C of manufacturing x watches is given by the formula C = 4000 + 2x, where the variable C is in dollars. (a) What is the cost of producing 1000 watches? (b) What is the cost of producing 2000 watches?

Balancing a Checkbook At the beginning of the month, Mike had a balance of $210 in his checking account. During the next month, he deposited $80, wrote a check for $120, made another deposit of $25, wrote two checks: one for $60 and the other for $32. He was also assessed a monthly service charge of $5. What was his balance at the end of the month?

In Problems 147 and 148, write an inequality using an absolute value to describe each statement. x is at least 6 units from 4.

In Problems 147 and 148, write an inequality using an absolute value to describe each statement. x is more than 5 units from 2.

U.S. Voltage In the United States, normal household voltage is 110 volts. It is acceptable for the actual voltage x to differ from normal by at most 5 volts. A formula that describes this is Ix - 1101 s 5 (a) Show that a voltage of 108 volts is acceptable. (b) Show that a voltage of 104 volts is not acceptable.

Foreign Voltage In other countries, normal household voltage is 220 volts. It is acceptable for the actual voltage x to differ from normal by at most 8 volts. A formula that describes this is Ix - 2201 s 8 (a) Show that a voltage of 214 volts is acceptable. (b) Show that a voltage of 209 volts is not acceptable.

Making PI'ecision Ball Bearings The F ireBall Company manufactures ball bearings for precision equipment. One of its products is a ball bearing with a stated radius of 3 centimeters (cm). Only ball bearings with a radius within 0.01 cm of this stated radius are acceptable. If x is the radius of a ball bearing, a formula describing this situation is Ix - 31 s 0.01 (a) Is a ball bearing of radius x = 2.999 acceptable? (b) Is a ball bearing of radius x = 2.89 acceptable?

Body Temperature Normal human body temperature is 98.6F. A temperature x that differs from normal by at least 1.5F is considered unhealthy.A formula that describes this is Ix - 98.61 1.5 (a) Show that a temperature of 97F is unhealthy. (b) Show that a temperature of 100F is not unhealthy

Distance from Earth to Its Moon The distance from Earth to the Moon is about 4 X 108 meters.* Express this distance as a whole number.

Height of Mt. Everest The height of Mt. Everest is 8872 meters: Express this height in scientific notation.

Wavelength of Visible Light The wavelength of visible light is about 5 X 10-7 meter.* Express this wavelength as a decimal.

Diameter of an Atom The diameter of an atom is about 1 X 10-10 meter.* Express this diameter as a decimal.

Diameter of Copper Wire The smallest commercial copper wire is about 0.0005 inch in diameter.T Express this diameter using scientific notation.

Smallest Motor The smallest motor ever made is less than 0.05 centimeter wide.t Express this width using scientific notation.

Astronomy One light-year is defined by astronomers to be the distance that a beam of light will travel in 1 year (365 days). If the speed of light is 186,000 miles per second, how many miles are in a light-year? Express your answer in scientific notation.

Astronomy How long does it take a beam of light to reach Earth from the Sun when the Sun is 93,000,000 miles from Earth? Express your answer in seconds, using scientific notation.

Does equal 0.333? If not, which is larger? By how much?

Does equal 0.666? If not, which is larger? By how much?

Is there a positive real number "closest" to O?

Number game I'm thinking of a number! It lies between 1 and 10; its square is rational and lies between 1 and 10. The number is larger than 7T. Correct to two decimal places (that is, truncated to two decimal places) name the number. Now think of your own number, describe it, and challenge a fellow student to name it.

Write a brief paragraph that illustrates the similarities and differences between "less than" ) and "less than or equal to" (s).

Give a reason why the statement 5 < 8 is true.

A(n) ____ triangle is one that contains an angle of 90 degrees. The longest side is called the ___ _

For a triangle with base b and altitude h, a formula for the area A is ___ _

The formula for the circumference C of a circle of radius r is _____.

Two triangles are ______ if corresponding angles are equal and the lengths of the corresponding sides are proportional.

True or False In a right triangle, the square of the length of the longest side equals the sum of the squares of the lengths of the other two sides.

True or False The triangle with sides of length 6, 8, and 10 is a right triangle.

True or False The volume of a sphere of radius r is 3 7Tr2.

True or False The triangles shown are congruent.

True or False The triangles shown are similar.

True or False The triangles shown are similar.

In Problems 11-16, the lengths of the legs of a right triangle are given. Find the hypotenuse. a = 5, b = 12

In Problems 11-16, the lengths of the legs of a right triangle are given. Find the hypotenuse. a = 6, b = 8

In Problems 11-16, the lengths of the legs of a right triangle are given. Find the hypotenuse. a = 10, b = 24

In Problems 11-16, the lengths of the legs of a right triangle are given. Find the hypotenuse. a = 4, b = 3

In Problems 11-16, the lengths of the legs of a right triangle are given. Find the hypotenuse. a = 7, b = 24

In Problems 11-16, the lengths of the legs of a right triangle are given. Find the hypotenuse. a = 14, b = 48

In Problems 17-24, the lengths of the sides of a triangle are given. Determine which are right triangles. For those that are, identify the hypotenuse. 3, 4, 5

In Problems 17-24, the lengths of the sides of a triangle are given. Determine which are right triangles. For those that are, identify the hypotenuse. 6, 8, 10

In Problems 17-24, the lengths of the sides of a triangle are given. Determine which are right triangles. For those that are, identify the hypotenuse. 4, 5, 6

In Problems 17-24, the lengths of the sides of a triangle are given. Determine which are right triangles. For those that are, identify the hypotenuse. 2, 2,3

In Problems 17-24, the lengths of the sides of a triangle are given. Determine which are right triangles. For those that are, identify the hypotenuse. 7, 24, 25

In Problems 17-24, the lengths of the sides of a triangle are given. Determine which are right triangles. For those that are, identify the hypotenuse. 10, 24,26

In Problems 17-24, the lengths of the sides of a triangle are given. Determine which are right triangles. For those that are, identify the hypotenuse. 6, 4, 3

In Problems 17-24, the lengths of the sides of a triangle are given. Determine which are right triangles. For those that are, identify the hypotenuse. 5, 4, 7

Find the area A of a rectangle with length 4 inches and width 2 inches.

Find the area A of a rectangle with length 9 centimeters and width 4 centimeters.

Find the area A of a triangle with height 4 inches and base 2 inches.

Find the area A of a triangle with height 9 centimeters and base 4 centimeters.

Find the area A and circumference C of a circle of radius 5 meters.

Find the area A and circumference C of a circle of radius 2 feet.

Find the volume V and surface area S of a rectangular box with length 8 feet, width 4 feet, and height 7 feet.

Find the volume V and surface area S of a rectangular box with length 9 inches, width 4 inches, and height 8 inches.

Find the volume V and surface area S of a sphere of radius 4 centimeters.

Find the volume V and surface area S of a sphere of radius 3 feet.

Find the volume V and surface area S of a right circular cylinder with radius 9 inches and height 8 inches.

Find the volume V and surface area S of a right circular cylinder with radius 8 inches and height 9 inches.

In Problems 37-40, find the area of the shaded region. 2 2 '0

In Problems 37-40, find the area of the shaded region. 2 '0 '0

In Problems 37-40, find the area of the shaded region. 2

In Problems 37-40, find the area of the shaded region. 2

In Problems 41-44, each pair of triangles is simila!: Find the missing length x and the missing angles A, B, and C. 90 4 30

In Problems 41-44, each pair of triangles is simila!: Find the missing length x and the missing angles A, B, and C. 16 v

In Problems 41-44, each pair of triangles is simila!: Find the missing length x and the missing angles A, B, and C. 45 30

In Problems 41-44, each pair of triangles is simila!: Find the missing length x and the missing angles A, B, and C. v

How many feet does a wheel with a diameter of 16 inches travel after four revolutions?

How many revolutions will a circular disk with a diameter of 4 feet have completed after it has rolled 20 feet?

In the figure shown, ABCD is a square, with each side of length 6 feet. The width of the border (shaded portion) between the outer square EFGH and ABCD is 2 feet. Find the area of the border. E F A B 0 -+- 0 C H G

Refer to the figure. Square ABCD has an area of 100 square feet; square BEFG has an area of 16 square feet. What is the area of the triangle CGF? o c

Architecture A Norman window consists of a rectangle surmounted by a semicircle. Find the area of the Norman window shown in the illustration. How much wood frame is needed to enclose the window? 6' 11--+---11 4

Construction A circular swimming pool, 20 feet in diameter, is enclosed by a wooden deck that is 3 feet wide. What is the area of the deck? How much fence is required to enclose the deck?

HowT.'111 Is the Great Pyramid'? The ancient Greek philosopher Thales of Miletus is reported on one occasion to have visited Egypt and calculated the height of the Great Pyramid of Cheops by means of shadow reckoning. Thales knew that each side of the base of the pyramid was 252 paces and that his own height was 2 paces. He measured the length of the pyramid's shadow to be 114 paces and determined the length of his shadow to be 3 paces. See the illustration. Using similar triangles, determine the height of the Great Pyramid in terms of the number of paces.

The Bermuda Triangle Karen is doing research on the Bermuda Triangle which she defines roughly by Hamilton, Bermuda; San Juan, Puerto Rico; and Fort Lauderdale, Florida. On her atlas Karen measures the straight-line distances from Hamilton to Fort Lauderdale, Fort Lauderdale to San Juan, and San Juan to Hamilton to be approximately 57 millimeters (mm), 58 mm, and 53.5 mm respectively. If the actual distance from Fort Lauderdale to San Juan is 1046 miles, approximate the actual distances from San Juan to Hamilton and from Hamilton to Fort Lauderdale.

In Problems 53-55, use the facts that the radius of Earth is 3960 miles and 1 mile = 5280 feet. How Far Can You See? The conning tower of the U.S.S. Silvers ides, a World War II submarine now permanently stationed in Muskegon, Michigan, is approximately 20 feet above sea level. How far can you see from the conning tower?

In Problems 53-55, use the facts that the radius of Earth is 3960 miles and 1 mile = 5280 feet. How Far Can You See'? A person who is 6 feet tall is standing on the beach in Fort Lauderdale, Florida, and looks out onto the Atlantic Ocean. Suddenly, a ship appears on the horizon. How far is the ship from shore?

In Problems 53-55, use the facts that the radius of Earth is 3960 miles and 1 mile = 5280 feet. How Far Can You See? The deck of a destroyer is 100 feet above sea level. How far can a person see from the deck? How far can a person see from the bridge, which is 150 feet above sea level?

Suppose that 117 and n are positive integers with 117 > n. If a = 1172 - n2, b = 2mn, and c = 1172 + /12, show that a, b, and c are the lengths of the sides of a right triangle. (This formula can be used to find the sides of a right triangle that are integers, such as 3,4, 5; 5, 12, 13; and so on. Such triplets of integers are called P ythagorean triples.)

You have 1000 feet of flexible pool siding and wish to construct a swimming pool. Experiment with rectangular-shaped pools with perimeters of 1000 feet. How do their areas vary? What is the shape of the rectangle with the largest area? Now compute the area enclosed by a circular pool with a perimeter (circumference) of 1000 feet. What would be your choice of shape for the pool? If rectangular, what is your preference for dimensions? Justify your choice. If your only consideration is to have a pool that encloses the most area, what shape should you use?

The Gibb's Hill Lighthouse, Southampton, Bermuda, in operation since 1846, stands 117 feet high on a hill 245 feet high, so its beam of light is 362 feet above sea level. A brochure states that the light itself can be seen on the horizon about 26 miles distant. Verify the correctness of this information. The brochure further states that ships 40 miles away can see the light and planes flying at 10,000 feet can see it 120 miles away. Verify the accuracy of these statements. What assumption did the brochure make about the height of the ship

The polynomial 3x4 - 2x3 + 13x2 - 5 is of degree __ . The leading coefficient is __ .

(x2 - 4)(x2 + 4) = __

(x - 2) (x2 + 2x + 4) = __ .

True or False 4[2 is a monomial of degree -2.

True or False The degree of the product of two nonzero polynomials equals the sum of their degrees.

True or False (x + a)(x2 + ax + a) = x3 + a3

In Problems 7-16, tell whether the expression is a monomial. If it is, name the variable(s) and the coefficient and give the degree of the monomial. If it is not a monomial state , why not. 2x3

In Problems 7-16, tell whether the expression is a monomial. If it is, name the variable(s) and the coefficient and give the degree of the monomial. If it is not a monomial state , why not. -4x2

In Problems 7-16, tell whether the expression is a monomial. If it is, name the variable(s) and the coefficient and give the degree of the monomial. If it is not a monomial state , why not. x

In Problems 7-16, tell whether the expression is a monomial. If it is, name the variable(s) and the coefficient and give the degree of the monomial. If it is not a monomial state , why not. -2x-3

In Problems 7-16, tell whether the expression is a monomial. If it is, name the variable(s) and the coefficient and give the degree of the monomial. If it is not a monomial state , why not. -2xi

In Problems 7-16, tell whether the expression is a monomial. If it is, name the variable(s) and the coefficient and give the degree of the monomial. If it is not a monomial state , why not. 5x2y3

In Problems 7-16, tell whether the expression is a monomial. If it is, name the variable(s) and the coefficient and give the degree of the monomial. If it is not a monomial state , why not. 8x y

In Problems 7-16, tell whether the expression is a monomial. If it is, name the variable(s) and the coefficient and give the degree of the monomial. If it is not a monomial state , why not. 2X2 - -3 Y

In Problems 7-16, tell whether the expression is a monomial. If it is, name the variable(s) and the coefficient and give the degree of the monomial. If it is not a monomial state , why not. x2 + y2

In Problems 7-16, tell whether the expression is a monomial. If it is, name the variable(s) and the coefficient and give the degree of the monomial. If it is not a monomial state , why not. 3x2 + 4

In Problems 1 7-26, tell whether the expression is a polynomial. 1f it is, give its degree. If it is not, state why not. 3x2 - 5

In Problems 1 7-26, tell whether the expression is a polynomial. 1f it is, give its degree. If it is not, state why not. 1 - 4x

In Problems 1 7-26, tell whether the expression is a polynomial. 1f it is, give its degree. If it is not, state why not. 5

In Problems 1 7-26, tell whether the expression is a polynomial. 1f it is, give its degree. If it is not, state why not. -7

In Problems 1 7-26, tell whether the expression is a polynomial. 1f it is, give its degree. If it is not, state why not. 3x2 - X

In Problems 1 7-26, tell whether the expression is a polynomial. 1f it is, give its degree. If it is not, state why not. . -+ 2 x

In Problems 1 7-26, tell whether the expression is a polynomial. 1f it is, give its degree. If it is not, state why not. 2y 3 - v

In Problems 1 7-26, tell whether the expression is a polynomial. 1f it is, give its degree. If it is not, state why not. 1 0z2 + z

In Problems 1 7-26, tell whether the expression is a polynomial. 1f it is, give its degree. If it is not, state why not. x2 + x -I

In Problems 1 7-26, tell whether the expression is a polynomial. 1f it is, give its degree. If it is not, state why not. 3x3 + 2x -1 ----=?:----- r-+x+1

In Problems 27-46, add, subtract, or multiply, as indicated. Express your answer as a single polynomial in standard form. ( x2 + 4x + 5) + ( 3x -3)

In Problems 27-46, add, subtract, or multiply, as indicated. Express your answer as a single polynomial in standard form. ( x3 + 3x2 + 2) + ( x2 - 4x + 4)

In Problems 27-46, add, subtract, or multiply, as indicated. Express your answer as a single polynomial in standard form. ( x3 - 2x2 + 5x + 10) -( 2x2 - 4x + 3)

In Problems 27-46, add, subtract, or multiply, as indicated. Express your answer as a single polynomial in standard form. ( x2 - 3x - 4) -( x3 -3x2 + X + 5)

In Problems 27-46, add, subtract, or multiply, as indicated. Express your answer as a single polynomial in standard form. ( 6x5 + x3 + x ) + ( 5x4 - x3 + 3x2 )

In Problems 27-46, add, subtract, or multiply, as indicated. Express your answer as a single polynomial in standard form. ( 10x5 - 8x2 ) + ( 3x3 - 2x2 + 6 )

In Problems 27-46, add, subtract, or multiply, as indicated. Express your answer as a single polynomial in standard form. ( x2 -3x + 1) + 2( 3x2 + X - 4)

In Problems 27-46, add, subtract, or multiply, as indicated. Express your answer as a single polynomial in standard form. -2( x2 + x + 1) + (-5x2 -X + 2)

In Problems 27-46, add, subtract, or multiply, as indicated. Express your answer as a single polynomial in standard form. 6 ( x3 + x2 - 3) - 4 ( 2x3 - 3x2 )

In Problems 27-46, add, subtract, or multiply, as indicated. Express your answer as a single polynomial in standard form. 8( 4x3 -3x2 -1) -6( 4x3 + 8x - 2)

In Problems 27-46, add, subtract, or multiply, as indicated. Express your answer as a single polynomial in standard form. ( x2 -x + 2) + ( 2x2 -3x + 5) -( x2 + 1)

In Problems 27-46, add, subtract, or multiply, as indicated. Express your answer as a single polynomial in standard form. ( x2 + 1) -( 4x2 + 5) + ( x2 + X - 2)

In Problems 27-46, add, subtract, or multiply, as indicated. Express your answer as a single polynomial in standard form. 9( i -3y + 4) -6( 1 -i)

In Problems 27-46, add, subtract, or multiply, as indicated. Express your answer as a single polynomial in standard form. 8( 1 -i) + 4( 1 + y + i + i)

In Problems 27-46, add, subtract, or multiply, as indicated. Express your answer as a single polynomial in standard form. x( x2 + x - 4)

In Problems 27-46, add, subtract, or multiply, as indicated. Express your answer as a single polynomial in standard form. 4x2 ( x3 - x + 2)

In Problems 27-46, add, subtract, or multiply, as indicated. Express your answer as a single polynomial in standard form. - 2x2 ( 4x3 + 5 )

In Problems 27-46, add, subtract, or multiply, as indicated. Express your answer as a single polynomial in standard form. 5x\3x - 4)

In Problems 27-46, add, subtract, or multiply, as indicated. Express your answer as a single polynomial in standard form. (x + 1)( x2 + 2x - 4)

In Problems 27-46, add, subtract, or multiply, as indicated. Express your answer as a single polynomial in standard form. ( 2x -3)( x2 + X + 1)

In Problems 47-64, multiply the polynomials using the FOIL method. Express your answer as a single polynomial in standard form. (x + 2)( x + 4)

In Problems 47-64, multiply the polynomials using the FOIL method. Express your answer as a single polynomial in standard form. (x + 3)( x + 5)

In Problems 47-64, multiply the polynomials using the FOIL method. Express your answer as a single polynomial in standard form. ( 2x + 5)( x + 2)

In Problems 47-64, multiply the polynomials using the FOIL method. Express your answer as a single polynomial in standard form. ( 3x + 1)( 2x + 1)

In Problems 47-64, multiply the polynomials using the FOIL method. Express your answer as a single polynomial in standard form. (x - 4)( x + 2)

In Problems 47-64, multiply the polynomials using the FOIL method. Express your answer as a single polynomial in standard form. (x + 4)( x - 2)

In Problems 47-64, multiply the polynomials using the FOIL method. Express your answer as a single polynomial in standard form. (x -3)( x - 2)

In Problems 47-64, multiply the polynomials using the FOIL method. Express your answer as a single polynomial in standard form. (x - 5)( x - 1)

In Problems 47-64, multiply the polynomials using the FOIL method. Express your answer as a single polynomial in standard form. ( 2x + 3)( x - 2)

In Problems 47-64, multiply the polynomials using the FOIL method. Express your answer as a single polynomial in standard form. ( 2x - 4)( 3x + 1)

In Problems 47-64, multiply the polynomials using the FOIL method. Express your answer as a single polynomial in standard form. (-2x + 3)( x - 4)

In Problems 47-64, multiply the polynomials using the FOIL method. Express your answer as a single polynomial in standard form. ( -3x - l)( x + 1)

In Problems 47-64, multiply the polynomials using the FOIL method. Express your answer as a single polynomial in standard form. (-x - 2)(-2x - 4)

In Problems 47-64, multiply the polynomials using the FOIL method. Express your answer as a single polynomial in standard form. (-2x -3)( 3 -x)

In Problems 47-64, multiply the polynomials using the FOIL method. Express your answer as a single polynomial in standard form. (x - 2y)( x + y)

In Problems 47-64, multiply the polynomials using the FOIL method. Express your answer as a single polynomial in standard form. ( 2x + 3y)( x - y)

In Problems 47-64, multiply the polynomials using the FOIL method. Express your answer as a single polynomial in standard form. (-2x -3y)( 3x + 2y)

In Problems 47-64, multiply the polynomials using the FOIL method. Express your answer as a single polynomial in standard form.

In Problems 65-88, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. (x - 7)( x + 7)

In Problems 65-88, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. (x - l)( x + 1)

In Problems 65-88, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. ( 2x + 3)( 2x - 3)

In Problems 65-88, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. ( 3x + 2)( 3x - 2)

In Problems 65-88, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. (x + 4)2

In Problems 65-88, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. (x + 5f

In Problems 65-88, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. (x - 4)2

In Problems 65-88, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. (x - 5)2

In Problems 65-88, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. ( 3x + 4)( 3x - 4)

In Problems 65-88, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. ( 5x - 3)( 5x + 3)

In Problems 65-88, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. ( 2x - 3f

In Problems 65-88, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. ( 3x - 4f

In Problems 65-88, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. (x + y)(x - y)

In Problems 65-88, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. (x + 3y)( x - 3y)

In Problems 65-88, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. ( 3x + y)( 3x - y)

In Problems 65-88, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. ( 3x + 4y)( 3x - 4y)

In Problems 65-88, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. (x + y)2

In Problems 65-88, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. (x - y?

In Problems 65-88, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. (x - 2y)2

In Problems 65-88, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. (2x + 3y)2

In Problems 65-88, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. (x - 2)3

In Problems 65-88, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. (x + 1 )3

In Problems 65-88, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. (2x + 1 )3

In Problems 65-88, multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form. (3x - 2)3

In Problems 89-104, find the quotient and the remainda Check your work by verifying that (Quotient)(Divisor) + Remainder = Dividend 4x3 - 3x2 + X + 1 divided by x + 2

In Problems 89-104, find the quotient and the remainda Check your work by verifying that (Quotient)(Divisor) + Remainder = Dividend 3x3 - x2 + X - 2 divided by x + 2

In Problems 89-104, find the quotient and the remainda Check your work by verifying that (Quotient)(Divisor) + Remainder = Dividend 4x3 - 3x2 + X + 1 divided by x2

In Problems 89-104, find the quotient and the remainda Check your work by verifying that (Quotient)(Divisor) + Remainder = Dividend 3x3 - x2 + X - 2 divided by x2

In Problems 89-104, find the quotient and the remainda Check your work by verifying that (Quotient)(Divisor) + Remainder = Dividend 5x4 - 3x2 + X + 1 divided by x2 + 2

In Problems 89-104, find the quotient and the remainda Check your work by verifying that (Quotient)(Divisor) + Remainder = Dividend 5x4 - x2 + X - 2 divided by x2 + 2

In Problems 89-104, find the quotient and the remainda Check your work by verifying that (Quotient)(Divisor) + Remainder = Dividend 4x5 - 3x2 + X + 1 divided by 2x3 - 1

In Problems 89-104, find the quotient and the remainda Check your work by verifying that (Quotient)(Divisor) + Remainder = Dividend 3x5 - x2 + X - 2 divided by 3x3 - 1

In Problems 89-104, find the quotient and the remainda Check your work by verifying that (Quotient)(Divisor) + Remainder = Dividend 2X4 - 3x3 + X + 1 divided by 2x2 + X + 1

In Problems 89-104, find the quotient and the remainda Check your work by verifying that (Quotient)(Divisor) + Remainder = Dividend 3x4 - x3 + X - 2 divided by 3x2 + X + 1

In Problems 89-104, find the quotient and the remainda Check your work by verifying that (Quotient)(Divisor) + Remainder = Dividend -4x3 + x2 - 4 divided by x - 1

In Problems 89-104, find the quotient and the remainda Check your work by verifying that (Quotient)(Divisor) + Remainder = Dividend -3x4 - 2x - 1 divided by x - 1

In Problems 89-104, find the quotient and the remainda Check your work by verifying that (Quotient)(Divisor) + Remainder = Dividend 1 - x2 + X 4 divided by x2 + X + 1

In Problems 89-104, find the quotient and the remainda Check your work by verifying that (Quotient)(Divisor) + Remainder = Dividend 1 - x2 + x4 divided by x2 - X + 1

In Problems 89-104, find the quotient and the remainda Check your work by verifying that (Quotient)(Divisor) + Remainder = Dividend x3 - a3 divided by x - a

In Problems 89-104, find the quotient and the remainda Check your work by verifying that (Quotient)(Divisor) + Remainder = Dividend x5 - a5 divided by x - a

Explain why the degree of the product of two nonzero polynomials equals the sum of their degrees.

Explain why the degree of the sum of two polynomials of different degrees equals the larger of their degrees.

Give a careful statement about the degree of the sum of two polynomials of the same degree.

Do you prefer adding two polynomials using the horizontal method or the vertical method? Write a brief position paper defending your choice.

Do you prefer to memorize the rule for the square of a binomial (x + a)2 or to use F OIL to obtain the product? Write a brief position paper defending your choice.

If factored completely, 3x3 - 12x = __ .

If a polynomial cannot be written as the product of two other polynomials (excluding 1 and -1), then the polynomial is said to be ____.

True or False The polynomial x2 + 4 is prime.

True or False 3x3 - 2x2 - 6x + 4 = (3x - 2)(x2 + 2).

In Problems 5-14, factor each polynomial by removing the common monomial factor. 3x + 6

In Problems 5-14, factor each polynomial by removing the common monomial factor. 7x - 14

In Problems 5-14, factor each polynomial by removing the common monomial factor. ax2 + a

In Problems 5-14, factor each polynomial by removing the common monomial factor. ax - a

In Problems 5-14, factor each polynomial by removing the common monomial factor. x3 + x2 + x

In Problems 5-14, factor each polynomial by removing the common monomial factor. x3 -x2 + x

In Problems 5-14, factor each polynomial by removing the common monomial factor. 2x2 - 2x

In Problems 5-14, factor each polynomial by removing the common monomial factor. 3x2 - 3x

In Problems 5-14, factor each polynomial by removing the common monomial factor. 3x2y - 6xy2 + 12xy

In Problems 5-14, factor each polynomial by removing the common monomial factor. 60x2y - 48xy2 + 72x3y

In Problems 15-22, factor the difference of two squares. x2 - 1

In Problems 15-22, factor the difference of two squares. x2 - 4

In Problems 15-22, factor the difference of two squares. 4x2 - 1

In Problems 15-22, factor the difference of two squares. 9x2 - 1

In Problems 15-22, factor the difference of two squares. x2 - 16

In Problems 15-22, factor the difference of two squares. x2 - 25

In Problems 15-22, factor the difference of two squares. 25x2 - 4

In Problems 15-22, factor the difference of two squares. 36x2 - 9

In Problems 23-32, factor the perfect squares. x2 + 2x + 1

In Problems 23-32, factor the perfect squares. x2 - 4x + 4

In Problems 23-32, factor the perfect squares. x2 + 4x + 4

In Problems 23-32, factor the perfect squares. x2 - 2x + 1

In Problems 23-32, factor the perfect squares. X2 - lax + 25

In Problems 23-32, factor the perfect squares. x2 + lOx + 25

In Problems 23-32, factor the perfect squares. 4x2 + 4x + 1

In Problems 23-32, factor the perfect squares. 9x2 + 6x + 1

In Problems 23-32, factor the perfect squares. 16x2 + 8x + 1

In Problems 23-32, factor the perfect squares. 25x2 + lax + 1

In Problems 33-38, factor the sum or difference of two cubes . x3 - 27

In Problems 33-38, factor the sum or difference of two cubes . x3 + 125

In Problems 33-38, factor the sum or difference of two cubes . x3 + 27

In Problems 33-38, factor the sum or difference of two cubes . 27 - 8x3

In Problems 33-38, factor the sum or difference of two cubes . 8x3 + 27

In Problems 33-38, factor the sum or difference of two cubes . 64 - 27x3

In Problems 39-50, factor each polynomial. x2 + 5x + 6

In Problems 39-50, factor each polynomial. x2 + 6x + 8

In Problems 39-50, factor each polynomial. x2 + 7x + 6

In Problems 39-50, factor each polynomial. x2 + 9x + 8

In Problems 39-50, factor each polynomial. x2 + 7 x + 10

In Problems 39-50, factor each polynomial. x2 + llx + 10

In Problems 39-50, factor each polynomial. x2 - lax + 16

In Problems 39-50, factor each polynomial. x2 - 17 x + 16

In Problems 39-50, factor each polynomial. x2 - 7x - 8

In Problems 39-50, factor each polynomial. x2 - 2x - 8

In Problems 39-50, factor each polynomial. x2 + 7x - 8

In Problems 39-50, factor each polynomial. x2 + 2x - 8

In Problems 51-56, factor by grouping. 2x2 + 4x + 3x + 6

In Problems 51-56, factor by grouping. 3x2 - 3x + 2x - 2

In Problems 51-56, factor by grouping. 2X2 - 4x + x - 2

In Problems 51-56, factor by grouping. 3x2 + 6x - x - 2

In Problems 51-56, factor by grouping. 6x2 + 9x + 4x + 6

In Problems 51-56, factor by grouping. 9x2 - 6x + 3x - 2

In Problems 57-68, factor each polynomial. 3X2 + 4x + 1

In Problems 57-68, factor each polynomial. 2x2 + 3x + 1

In Problems 57-68, factor each polynomial. 2z2 + 5z + 3

In Problems 57-68, factor each polynomial. pz,2 + 5z + 1

In Problems 57-68, factor each polynomial. 3x2 + 2x - 8

In Problems 57-68, factor each polynomial. 3x2 + lax + 8

In Problems 57-68, factor each polynomial. 3x2 - 2x - 8

In Problems 57-68, factor each polynomial. 3x2 - lax + 8

In Problems 57-68, factor each polynomial. Ux2 + 14x + 8

In Problems 57-68, factor each polynomial. 3x2 - 14x + 8

In Problems 57-68, factor each polynomial. 3x2 + lax - 8

In Problems 57-68, factor each polynomial. 3x2 - lax - 8

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. x2 - 36

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. x2 - 9

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. 2 - 8x2

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. 3 - 27 x2

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. x2 + llx + 10

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. x2 + 5x + 4

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. x2 - lax + 21

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. x2 - 6x + 8

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. 4x2 - 8x + 32

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. 3x2 - 12x + 15

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. x2 + 4x + 16

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. x2 + 12x + 36

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. 15 + 2x - x2

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. 14 + 6x - x2

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. x2 - 12x - 36

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. x3 + 8x2 - 20x

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. l + lli + 30i

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. 3i - 18i - 48y

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. 4x2 + 12x + 9

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. 9x2 - 12x + 4

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. 6x 2 + 8x + 2

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. 8x2 + 6x - 2

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. X4 - 81

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. X4 - 1

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. x6 - 2x3 + 1

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. x6 + 2x3 + 1

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. x7 - x5

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. x8 - xS

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. 16x2 + 24x + 9

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. 9x2 - 24x + 16

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. 5 + 16x - 16x2

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. 5 + llx - 16x2

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. 41 - 16y + 15

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. 91 + 9y - 4

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. 1 - 8x2 - 9x4

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. 4 - 14x2 - 8x4

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. x(x + 3) - 6(x + 3)

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. 5 (3x - 7) + x(3x - 7)

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. (x + 2f - 5(x + 2)

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. (x - 1 )2 - 2(x - 1)

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. (3x - 2)3 - 27

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. (5x + 1 )3 - 1

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. 3(x2 + lOx + 25) - 4(x + 5)

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. 7(x2 - 6x + 9) + 5(x - 3)

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. x3 + 2x2 - X - 2

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. x3 - 3x2 - X + 3

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. x4 - x3 + x - 1

In Problems 69-116, factor completely each polynomial. If the polynomial cannot be factored, say it is prime. X4 + x3 + X + 1

In Problems 117-126, expressions that occur in calculus are given. Faclor completely each expression. 2(3x + 4)2 + (2x + 3) ' 2(3x + 4) '3

In Problems 117-126, expressions that occur in calculus are given. Faclor completely each expression. 5(2x + 1 )2 + (5x - 6) 2(2x + 1) '2

In Problems 117-126, expressions that occur in calculus are given. Faclor completely each expression. 2x(2x + 5) + x2 . 2

In Problems 117-126, expressions that occur in calculus are given. Faclor completely each expression. 3x2 (8x - 3) + x3 8

In Problems 117-126, expressions that occur in calculus are given. Faclor completely each expression. 2(x + 3)(x - 2)3 + (x + 3)2 . 3(x - 2)2

In Problems 117-126, expressions that occur in calculus are given. Faclor completely each expression. 4(x + 5)3(x _ 1 )2 + (x + 5t 2(x - 1)

In Problems 117-126, expressions that occur in calculus are given. Faclor completely each expression. (4x - 3)2 + x ' 2(4x - 3) 4

In Problems 117-126, expressions that occur in calculus are given. Faclor completely each expression. 3x2(3x + 4)2 + x3 . 2(3x + 4) 3

In Problems 117-126, expressions that occur in calculus are given. Faclor completely each expression. 2(3x - 5) ' 3(2x + 1 )3 + (3x - 5)2 . 3(2x + 1 )22

In Problems 117-126, expressions that occur in calculus are given. Faclor completely each expression. 3(4x + 5f 4(5x + 1 )2 + (4x + 5)3 2(5x + 1 ) '5

Show that x2 + 4 is prime.

Show that x2 + 4 is prime.

Make up a polynomial that factors into a perfect square.

Explain to a fellow student what you look for first when presented with a factoring problem. What do you do next?

To check division, the expression that is being divided, the dividend, should equal the p{6duct of the ____ and the ____ plus the ___.

To divide 2x3 - 5x + 1 by x + 3 using synthetic division, the first step is to write ____ ).

True or False " In using synthetic division, the divisor is always a polynomial of degree 1, whose leading coefficient is 1.

True or False ) 32 5x3 + 3x2 + 2x + l ) 6 -31 -2 5 1 means = 5x- 7x + 1 + --. x+2 x+2 -10 14 -32 5 -7 16 -31

In Problems 5-16, use synthetic division to find the quotient and remainder when: x3 - x2 + 2x + 4 is divided by x - 2

In Problems 5-16, use synthetic division to find the quotient and remainder when: x3 + 2x2 - 3x + 1 is divided by x + 1

In Problems 5-16, use synthetic division to find the quotient and remainder when: 3x3 + 2x2 - X + 3 is divided by x - 3

In Problems 5-16, use synthetic division to find the quotient and remainder when: -4x3 + 2x2 - X + 1 is divided by x + 2

In Problems 5-16, use synthetic division to find the quotient and remainder when: x5 - 4x3 + x is divided by x + 3

In Problems 5-16, use synthetic division to find the quotient and remainder when: X4 + x2 + 2 is divided by x - 2

In Problems 5-16, use synthetic division to find the quotient and remainder when: 4x6 - 3x4 + x2 + 5 is divided by x - 1

In Problems 5-16, use synthetic division to find the quotient and remainder when: x5 + 5x3 - 10 is divided by x + 1

In Problems 5-16, use synthetic division to find the quotient and remainder when: 0.lx3 + 0.2x is divided by x + 1 .1

In Problems 5-16, use synthetic division to find the quotient and remainder when: 0.1x2 - 0.2 is divided by x + 2.1

In Problems 5-16, use synthetic division to find the quotient and remainder when: x5 - 1 is divided by x - 1

In Problems 5-16, use synthetic division to find the quotient and remainder when: x5 + 1 is divided by x + 1

In Problems 17-26, use synthetic division to determine whether x - c is a factor of the given polynomial. 4x3 - 3x2 - 8x + 4; x - 2

In Problems 17-26, use synthetic division to determine whether x - c is a factor of the given polynomial. -4x3 + 5x2 + 8; x + 3

In Problems 17-26, use synthetic division to determine whether x - c is a factor of the given polynomial. 3x4 - 6x3 - 5x + 10; x - 2

In Problems 17-26, use synthetic division to determine whether x - c is a factor of the given polynomial. 4X4 - 1 5x2 - 4; x - 2

In Problems 17-26, use synthetic division to determine whether x - c is a factor of the given polynomial. 3x6 + 82x3 + 27; x + 3

In Problems 17-26, use synthetic division to determine whether x - c is a factor of the given polynomial. 2x6 - 1 8x4 + x2 - 9; x + 3

In Problems 17-26, use synthetic division to determine whether x - c is a factor of the given polynomial. 4x6 - 64x4 + x2 - 15; x + 4

In Problems 17-26, use synthetic division to determine whether x - c is a factor of the given polynomial. x6 - 1 6x4 + x2 - 1 6; x + 4

In Problems 17-26, use synthetic division to determine whether x - c is a factor of the given polynomial. x6 - 1 6x4 + x2 - 1 6; x + 4

In Problems 17-26, use synthetic division to determine whether x - c is a factor of the given polynomial. 3x4 + x3 - 3x + 1; 1 x + -

Find the sum of a, b, C, and d if ------- x3 - 2X2 + 3x + 5? d x+2 = ax- + bx + C +--x+2

When dividing a polynomial by x - c, do you prefer to use long division or synthetic division? Does the value of C make a difference to you in choosing? Give reasons.

When the numerator and denominator of a rational expression contain no common factors (except 1 and -1), the rational expression is in __ ___ .

LCM is an abbreviation for __ ___ _

True or False The rational expression 2 is reduced to lowest terms

Trite or False The LCM of 2x3 + 6x2 and 6x4 + 4x3 is 4x3(x + 1).

In Problems 5-16, reduce each rational expression to lowest terms. 3x + 9 x2 - 1

In Problems 5-16, reduce each rational expression to lowest terms. 4x2 + 8x 12x + 24

In Problems 5-16, reduce each rational expression to lowest terms. x2 - 2x " 3x - 6

In Problems 5-16, reduce each rational expression to lowest terms. 15x2 + 24x --::-?- 3x

In Problems 5-16, reduce each rational expression to lowest terms. 12x- 6x

In Problems 5-16, reduce each rational expression to lowest terms. x2 + 4x + 4 X 2 - 4

In Problems 5-16, reduce each rational expression to lowest terms. l - 25 2y 2 - 8y - 10

In Problems 5-16, reduce each rational expression to lowest terms. 31 - y - 2 :----'--- 3y- + 5y + 2

In Problems 5-16, reduce each rational expression to lowest terms. x2 + 4x - 5 , . x2 - 2x + 1

In Problems 5-16, reduce each rational expression to lowest terms. x - x2 x + x 2 --- 2

In Problems 5-16, reduce each rational expression to lowest terms. x2 + 5x - 14 2-x

In Problems 5-16, reduce each rational expression to lowest terms. 2x2 + 5x - 3 1 1 - 2x

In Problems 1 7-34, pelform the indicated operation and simplify the result. Leave your answer in factored form. 3x + 6 x . x2 - 4

In Problems 1 7-34, pelform the indicated operation and simplify the result. Leave your answer in factored form. 3 x2 2x ' 6x + 10

In Problems 1 7-34, pelform the indicated operation and simplify the result. Leave your answer in factored form. 4x2 x3 - 64 x2 _ 16 2x

In Problems 1 7-34, pelform the indicated operation and simplify the result. Leave your answer in factored form. 12 x3 + 1 x2 + X 4x - 2

In Problems 1 7-34, pelform the indicated operation and simplify the result. Leave your answer in factored form. 4x - 8 12 K' 12-6x

In Problems 1 7-34, pelform the indicated operation and simplify the result. Leave your answer in factored form. 6x - 27 2 --- 5x 4x - 18

In Problems 1 7-34, pelform the indicated operation and simplify the result. Leave your answer in factored form. x2 - 3x - 10 x2 + 4x - 21 x + 2 2x - 35 x 2 + 9x + 14

In Problems 1 7-34, pelform the indicated operation and simplify the result. Leave your answer in factored form. 2 + x - 6 x2 - 25 ----- x2 + 4x - 5 x2 + 2x - 15

In Problems 1 7-34, pelform the indicated operation and simplify the result. Leave your answer in factored form. 6x x2 - 4 3x - 9 2x + 4

In Problems 1 7-34, pelform the indicated operation and simplify the result. Leave your answer in factored form. 12x 5x + 20 ---=-4x2 x2 - 16

In Problems 1 7-34, pelform the indicated operation and simplify the result. Leave your answer in factored form. 8x 2x2 - 1 lOx x + 1

In Problems 1 7-34, pelform the indicated operation and simplify the result. Leave your answer in factored form. x-2 4x x2 - 4x + 4 12x

In Problems 1 7-34, pelform the indicated operation and simplify the result. Leave your answer in factored form. 4-x 4+x --- 4x x2 - 16

In Problems 1 7-34, pelform the indicated operation and simplify the result. Leave your answer in factored form. 3 + x 3-x X - 9 2- 9x3

In Problems 1 7-34, pelform the indicated operation and simplify the result. Leave your answer in factored form. x2 + 7x + 12 x2 - 7x + 12 -'..:..- ----'= x2 + X - 12 x2 - x - 12

In Problems 1 7-34, pelform the indicated operation and simplify the result. Leave your answer in factored form. x2 + 7x + 6 x2 + x - 6 x2 + 5x - 6 x2 + 5x + 6

In Problems 1 7-34, pelform the indicated operation and simplify the result. Leave your answer in factored form. 2x2 - x - 28 3x2 - x - 2 ,---- --- 4x2 + 1 6x + 7 3x2 + 11x + 6

In Problems 1 7-34, pelform the indicated operation and simplify the result. Leave your answer in factored form. 9x2 + 3x - 2 12x2 + 5x - 2 -::-- --- 9x2 - 6x + 1 8x2 - lOx - 3

In Problems 35-52, perform [he indicated operation and simplify the result. Leave your answer in factored form. x 5 - 2 2 + -

In Problems 35-52, perform [he indicated operation and simplify the result. Leave your answer in factored form. 3 6 - x x

In Problems 35-52, perform [he indicated operation and simplify the result. Leave your answer in factored form. x2 4 --2x - 3 ---2x - 3

In Problems 35-52, perform [he indicated operation and simplify the result. Leave your answer in factored form. 3x2 9 --- 2x - 1 2x- 1

In Problems 35-52, perform [he indicated operation and simplify the result. Leave your answer in factored form. x + 1 2x - 3 --x-3 +--x - 3

In Problems 35-52, perform [he indicated operation and simplify the result. Leave your answer in factored form. 2x - 5 x + 4 --3x + 2 +--3x + 2

In Problems 35-52, perform [he indicated operation and simplify the result. Leave your answer in factored form. 3x + 5 2x - 4 --- -- 2x - 1 2x - 1

In Problems 35-52, perform [he indicated operation and simplify the result. Leave your answer in factored form. 5x - 4 x + 1 --3x + 4 ---3x + 4

In Problems 35-52, perform [he indicated operation and simplify the result. Leave your answer in factored form. 4 x --x-2 + -- 2-x

In Problems 35-52, perform [he indicated operation and simplify the result. Leave your answer in factored form. 6 x -- - x-I --I - x

In Problems 35-52, perform [he indicated operation and simplify the result. Leave your answer in factored form. 4 2 -- x - I - -x+2

In Problems 35-52, perform [he indicated operation and simplify the result. Leave your answer in factored form. 2 5 --x+5 ---x-5

In Problems 35-52, perform [he indicated operation and simplify the result. Leave your answer in factored form. x 2x - 3 . . --x+l +--x-I

In Problems 35-52, perform [he indicated operation and simplify the result. Leave your answer in factored form. 3x 2x --x - 4 + -- x+3

In Problems 35-52, perform [he indicated operation and simplify the result. Leave your answer in factored form. x-3 x+4 --x+2 ---x-2

In Problems 35-52, perform [he indicated operation and simplify the result. Leave your answer in factored form. 2x - 3 2x + 1 . - x+l

In Problems 35-52, perform [he indicated operation and simplify the result. Leave your answer in factored form. x 1 --+ - x2 - 4 x

In Problems 35-52, perform [he indicated operation and simplify the result. Leave your answer in factored form. x-I x --x3 +--x2 +1

[n Problems 53-60, find the LCM of the given polynomials. x2 - 4, x2 - X - 2

[n Problems 53-60, find the LCM of the given polynomials. x2 - x - 12, x2 - 8x + 16

[n Problems 53-60, find the LCM of the given polynomials. x3 - x, x2 - x

[n Problems 53-60, find the LCM of the given polynomials. 3x2 - 27, 2x2 - X - 15

[n Problems 53-60, find the LCM of the given polynomials. 4x3 - 4x2 + x, 2x3 - x2, x3

[n Problems 53-60, find the LCM of the given polynomials. x - 3, x2 + 3x, x3 - 9x

[n Problems 53-60, find the LCM of the given polynomials. x3 - x, x3 - 2x2 + x, x3 - 1

[n Problems 53-60, find the LCM of the given polynomials. x2 + 4x + 4, x3 + 2x2, (x + 2)4

In Problems 61-72, pelform the indicated operations and simplify the result. Leave your answer in factored form. X x2 - 7x + 6 x2 - 2x - 24

In Problems 61-72, pelform the indicated operations and simplify the result. Leave your answer in factored form. x x + 1 -- - , ---- x - 3 r + 5x - 24

In Problems 61-72, pelform the indicated operations and simplify the result. Leave your answer in factored form. 4x - 2 ---- x2 - 4 x2 - 6

In Problems 61-72, pelform the indicated operations and simplify the result. Leave your answer in factored form. - x - 4 x-I x2 - 2x+l

In Problems 61-72, pelform the indicated operations and simplify the result. Leave your answer in factored form. 3 2 2 + (x - 1 ) (x + 1 ) (x - 1)(x + 1)

In Problems 61-72, pelform the indicated operations and simplify the result. Leave your answer in factored form. 2 _ 6 (x + 2)2(x - 1) (x + 2 )(x - 1 )2

In Problems 61-72, pelform the indicated operations and simplify the result. Leave your answer in factored form. x + 4 2x + 3 --- r-x-2 x2 + 2x - 8

In Problems 61-72, pelform the indicated operations and simplify the result. Leave your answer in factored form. 2x - 3 x - 2 ---- x2 + 8x + 7 (x + 1 f

In Problems 61-72, pelform the indicated operations and simplify the result. Leave your answer in factored form. .!. _ 2_ + 3 x x2 +x x3 - X2

In Problems 61-72, pelform the indicated operations and simplify the result. Leave your answer in factored form. x + 2 - x + 1 ---- x- 1 x3x2

In Problems 61-72, pelform the indicated operations and simplify the result. Leave your answer in factored form. 1 ( 1 1 ) . h x+h x

In Problems 61-72, pelform the indicated operations and simplify the result. Leave your answer in factored form. .!. [ 1 - J . h (x + hi

In Problems 73-84, perform the indicated operations and simplify the result. Leave your answer in factored form. 1 + 1 - -

In Problems 73-84, perform the indicated operations and simplify the result. Leave your answer in factored form. 4 + - 3--

In Problems 73-84, perform the indicated operations and simplify the result. Leave your answer in factored form. 2 _ x+1 3 + x

In Problems 73-84, perform the indicated operations and simplify the result. Leave your answer in factored form. 1 _ _ _o _ x x2 X X + 1 2 ---x

In Problems 73-84, perform the indicated operations and simplify the result. Leave your answer in factored form. x+4 - -x-3 x - 2 x + 1 x + 1

In Problems 73-84, perform the indicated operations and simplify the result. Leave your answer in factored form. x-2 x x + 1 x-2 x+3

In Problems 73-84, perform the indicated operations and simplify the result. Leave your answer in factored form. x-2 x-1 x x+2 +-x+1

In Problems 73-84, perform the indicated operations and simplify the result. Leave your answer in factored form. 2x + 5 --- -x-2 x-1 x ? (x + 1 )2

In Problems 73-84, perform the indicated operations and simplify the result. Leave your answer in factored form.1 ---1 1 - x

In Problems 73-84, perform the indicated operations and simplify the result. Leave your answer in factored form. 1 --1 - 1 1 ---1 - x

In Problems 73-84, perform the indicated operations and simplify the result. Leave your answer in factored form. 2(x - 1)-1 + 3 --=-- 3(x -----'--- - 1t) + 2

In Problems 73-84, perform the indicated operations and simplify the result. Leave your answer in factored form. 4(x + 2) 1 - 3 --=-- 3(x + -----'-- 2)---) 1 - 1

In Problems 85-92, expressions that occur in calculus are given. Reduce each expression to lowest terms. 2x + 3) 3 - (3 - 5) 2

In Problems 85-92, expressions that occur in calculus are given. Reduce each expression to lowest terms. (4x + 1)5 - (5x - 2) 4 (5x - 2)

In Problems 85-92, expressions that occur in calculus are given. Reduce each expression to lowest terms. x2x - (x2 + 1 ) 1 x2+1t

In Problems 85-92, expressions that occur in calculus are given. Reduce each expression to lowest terms. x . 2x - (X l - 4) . 1 (x2 - 4t

In Problems 85-92, expressions that occur in calculus are given. Reduce each expression to lowest terms. (3x + 1) 2x - x2 3 (3x + 1 )2

In Problems 85-92, expressions that occur in calculus are given. Reduce each expression to lowest terms. (2x - 5) 3x2 - x3. 2 ?

In Problems 85-92, expressions that occur in calculus are given. Reduce each expression to lowest terms. (x2 + 1 ) 3 - (3x + 4) 2x ? (x2 + 1

In Problems 85-92, expressions that occur in calculus are given. Reduce each expression to lowest terms. (X l + 9) 2 - (2x - 5) 2x ? (x2 + 9t

The Lensmaker's Equation The focal length f of a lens with index of refraction n is 1 [ 1 1 ] - = (n - 1) -- + -- f RI R 2 where R) and Rl are the radii of curvature of the front and back surfaces of the lens. Express f as a rational expression. Evaluate the rational expression for n = 1.5, R) = 0.1 meter, and Rl = 0.2 meter.

Electrical Circuits An electrical circuit contains three resistors connected in parallel. If the resistance of each is R1 , Rz , and R3 ohms, respectively, their combined resistance R is given by the formula 1 1 1 1 -=--+-- + - R RJ R2 R3 Express R as a rational expression. Evaluate R for RJ = 5 ohms, R2 = 4 ohms, and R3 = 10 ohms.

The following expressions are called continued fractions: 1 (X l + 9) 2 - (2x - 5) 2x 92. ? (x2 + 9t 94. Electrical Circuits An electrical circuit contains three resistors connected in parallel. If the resistance of each is R1 , Rz , and R3 ohms, respectively, their combined resistance R is given by the formula 1 1 1 1 -=--+-- + - R RJ R2 R3 Express R as a rational expression. Evaluate R for RJ = 5 ohms, R2 = 4 ohms, and R3 = 10 ohms. 1 1 1 + - x' 1 1 +--1 ' 1 + x 1 + ------ 1 + --- --- 1 Each simplifies to an expression of the form 1 1 +--1 1 + x ax + b bx + c 1 + ------ 1 1 +--1 1 + x Trace the successive values of a, b, and c as you "continue" the fraction. Can you discover the patterns that these values follow? Go to the library and research Fibonacci numbers. Write a report on your findings.

Explain to a fellow student when you would use the LCM method to add two rational expressions. Give two examples of adding two rational expressions, one in which you use the LCM and the other in which you do not.

Which of the two methods given in the text for simplifying complex rational expressions do you prefer? Write a brief paragraph stating the reasons for your choice.

(-3)2 = __ ; -32 = __ (pp. 2 1-24)

Vi6 = __ ; v(=4)2 = __ (pp. 21-24)

In the symbol -Va, the integer n is called the __ .

True or False = -2

\ We call .;ya the ____ of a.

True or False = -3

In Problems 7-42, simplify each expression. Assume thai all variables are positive when they appear. V27

In Problems 7-42, simplify each expression. Assume thai all variables are positive when they appear. V16

In Problems 7-42, simplify each expression. Assume thai all variables are positive when they appear. V-8

In Problems 7-42, simplify each expression. Assume thai all variables are positive when they appear. V-1

In Problems 7-42, simplify each expression. Assume thai all variables are positive when they appear. Vs8

In Problems 7-42, simplify each expression. Assume thai all variables are positive when they appear. \54

In Problems 7-42, simplify each expression. Assume thai all variables are positive when they appear. V-8x

In Problems 7-42, simplify each expression. Assume thai all variables are positive when they appear. V48x5

In Problems 7-42, simplify each expression. Assume thai all variables are positive when they appear. Vx12y8

In Problems 7-42, simplify each expression. Assume thai all variables are positive when they appear. Vx10y5

In Problems 7-42, simplify each expression. Assume thai all variables are positive when they appear. Vx9yy --- xy3

In Problems 7-42, simplify each expression. Assume thai all variables are positive when they appear. V3xy2 --- 81x4y2

In Problems 7-42, simplify each expression. Assume thai all variables are positive when they appear. V36x

In Problems 7-42, simplify each expression. Assume thai all variables are positive when they appear. V9x5

In Problems 7-42, simplify each expression. Assume thai all variables are positive when they appear. V3.?V12x

In Problems 7-42, simplify each expression. Assume thai all variables are positive when they appear. V5x V20x3

In Problems 7-42, simplify each expression. Assume thai all variables are positive when they appear. NVs)2

In Problems 7-42, simplify each expression. Assume thai all variables are positive when they appear. (\13 ViOt

In Problems 7-42, simplify each expression. Assume thai all variables are positive when they appear. (3V6)(2v2)

In Problems 7-42, simplify each expression. Assume thai all variables are positive when they appear. (5Vs)( -3\1'3)

In Problems 7-42, simplify each expression. Assume thai all variables are positive when they appear. 3v2 + 4v

In Problems 7-42, simplify each expression. Assume thai all variables are positive when they appear. 6V5 - 4V5

In Problems 7-42, simplify each expression. Assume thai all variables are positive when they appear. -V18 + 2V

In Problems 7-42, simplify each expression. Assume thai all variables are positive when they appear. 2vTI -3V

In Problems 7-42, simplify each expression. Assume thai all variables are positive when they appear. (\1'3 + 3)(\1'3 - 1 )

In Problems 7-42, simplify each expression. Assume thai all variables are positive when they appear. (Vs - 2) (Vs + 3)

In Problems 7-42, simplify each expression. Assume thai all variables are positive when they appear. 5\12 - 2\154

In Problems 7-42, simplify each expression. Assume thai all variables are positive when they appear. 9 V24 - V

In Problems 7-42, simplify each expression. Assume thai all variables are positive when they appear. (Vx - 1 ) 2

In Problems 7-42, simplify each expression. Assume thai all variables are positive when they appear. (Vx + Vs)2

In Problems 7-42, simplify each expression. Assume thai all variables are positive when they appear. V16x4 - V2x

In Problems 7-42, simplify each expression. Assume thai all variables are positive when they appear. \Y32x +

In Problems 7-42, simplify each expression. Assume thai all variables are positive when they appear. v3 - 3 v

In Problems 7-42, simplify each expression. Assume thai all variables are positive when they appear. 3xv9Y + 4 v

In Problems 7-42, simplify each expression. Assume thai all variables are positive when they appear. -3X+5

In Problems 7-42, simplify each expression. Assume thai all variables are positive when they appear. 8xy - V25x2/ + V8x3i

In Problems 43-54, rationalize the denominator of each expression. Assume that all variables are positive when they appear. 1 v2

In Problems 43-54, rationalize the denominator of each expression. Assume that all variables are positive when they appear. 2 \1'3

In Problems 43-54, rationalize the denominator of each expression. Assume that all variables are positive when they appear. -\3 V5

In Problems 43-54, rationalize the denominator of each expression. Assume that all variables are positive when they appear. -\3 V8

In Problems 43-54, rationalize the denominator of each expression. Assume that all variables are positive when they appear. V3 5 - V2

In Problems 43-54, rationalize the denominator of each expression. Assume that all variables are positive when they appear. v2 , r.:. v7 + 2

In Problems 43-54, rationalize the denominator of each expression. Assume that all variables are positive when they appear. 2 - V5 2 + 3V5

In Problems 43-54, rationalize the denominator of each expression. Assume that all variables are positive when they appear. \1'3 - 1 , t::. 2 v3 + 3

In Problems 43-54, rationalize the denominator of each expression. Assume that all variables are positive when they appear. 5 V2

In Problems 43-54, rationalize the denominator of each expression. Assume that all variables are positive when they appear. -2 \9

In Problems 43-54, rationalize the denominator of each expression. Assume that all variables are positive when they appear. Vx+h. Vx+h. - \IX + \

In Problems 43-54, rationalize the denominator of each expression. Assume that all variables are positive when they appear. Vx+h+ vx+h - vx -h

In ProbLems 55-66, simpLify each expression. 82/3

In ProbLems 55-66, simpLify each expression. 43/2

In ProbLems 55-66, simpLify each expression. -27) 1/3

In ProbLems 55-66, simpLify each expression. 163/4

In ProbLems 55-66, simpLify each expression. 163/2

In ProbLems 55-66, simpLify each expression. 253/2

In ProbLems 55-66, simpLify each expression. 9 -3/2

In ProbLems 55-66, simpLify each expression. 16-3/2

(-3)2 = __ ; -32 = __

In ProbLems 55-66, simpLify each expression. (27)2/3

In ProbLems 55-66, simpLify each expression. 8 -3/2

In ProbLems 55-66, simpLify each expression. ( 8 )-2/3

In Problems 67-74, simplify each expression. Express your answer so that only positive exponents occur. Assume that the variables are positive. x3/4XI/3x-I/2

In Problems 67-74, simplify each expression. Express your answer so that only positive exponents occur. Assume that the variables are positive. x2/3 x1/2 x-1/4

In Problems 67-74, simplify each expression. Express your answer so that only positive exponents occur. Assume that the variables are positive. (x3y6)1/3

In Problems 67-74, simplify each expression. Express your answer so that only positive exponents occur. Assume that the variables are positive. (x4y8)3/4

In Problems 67-74, simplify each expression. Express your answer so that only positive exponents occur. Assume that the variables are positive. (x2y)1/3 (xy2)2/3 ---- x2/3y3/2

In Problems 67-74, simplify each expression. Express your answer so that only positive exponents occur. Assume that the variables are positive. (xy)1/4 (x2y2)1/2 --- (x2y)3/4

In Problems 67-74, simplify each expression. Express your answer so that only positive exponents occur. Assume that the variables are positive. (16x2y-1/3)3/4 --- (xy2)1/4

In Problems 67-74, simplify each expression. Express your answer so that only positive exponents occur. Assume that the variables are positive. (4x-1y1/3)3/2 --- (xy)3/2

In Problems 75-88, expressions thaI occur in calculus are given. Write each expression as a single quotient in which only positive exponents and/or radicals appear. X . ? + 2(1 + x)I /2 x > -1 f' (1 + x)l/

In Problems 75-88, expressions thaI occur in calculus are given. Write each expression as a single quotient in which only positive exponents and/or radicals appear. 1 + x -1/2 1 /2 + x 2x x>o

In Problems 75-88, expressions thaI occur in calculus are given. Write each expression as a single quotient in which only positive exponents and/or radicals appear. 2x (x2+1)1/2 + x2 + 1)1/2 2x

In Problems 75-88, expressions thaI occur in calculus are given. Write each expression as a single quotient in which only positive exponents and/or radicals appear. x + 1)1/3 + x. '! . '(x + 1t2/3 x"* -1

In Problems 75-88, expressions thaI occur in calculus are given. Write each expression as a single quotient in which only positive exponents and/or radicals appear. . 1 +. 1 2

In Problems 75-88, expressions thaI occur in calculus are given. Write each expression as a single quotient in which only positive exponents and/or radicals appear. x"* 2,x"* - 8'

In Problems 75-88, expressions thaI occur in calculus are given. Write each expression as a single quotient in which only positive exponents and/or radicals appear. 1 x -== ( 2 , 1 + x

In Problems 75-88, expressions thaI occur in calculus are given. Write each expression as a single quotient in which only positive exponents and/or radicals appear. 2x V x" + 1 - x ----= == 2 --- - - r +

In Problems 75-88, expressions thaI occur in calculus are given. Write each expression as a single quotient in which only positive exponents and/or radicals appear. (x + 4)1/2 - 2x(x + 4tl/2 - x + 4 x> -1 x> -4

In Problems 75-88, expressions thaI occur in calculus are given. Write each expression as a single quotient in which only positive exponents and/or radicals appear. -3 < x < 3

In Problems 75-88, expressions thaI occur in calculus are given. Write each expression as a single quotient in which only positive exponents and/or radicals appear. x < -1 or x> 1

In Problems 75-88, expressions thaI occur in calculus are given. Write each expression as a single quotient in which only positive exponents and/or radicals appear. x2+4)1/2 - x2(9-x2)-1/2 --- 9-x2

In Problems 75-88, expressions thaI occur in calculus are given. Write each expression as a single quotient in which only positive exponents and/or radicals appear. x>O

In Problems 75-88, expressions thaI occur in calculus are given. Write each expression as a single quotient in which only positive exponents and/or radicals appear. x"*-1,x"*1

In Problems 89-98, expressions that occur in calculus are given. Factor each expression. Express your answer so that only positive exponents occur. (x + 1)3/2 + x'(x + 1) 1 /2 X 2: -1

In Problems 89-98, expressions that occur in calculus are given. Factor each expression. Express your answer so that only positive exponents occur. (x2 + 4)4/3 + x' (x2 + 4//3'2x

In Problems 89-98, expressions that occur in calculus are given. Factor each expression. Express your answer so that only positive exponents occur. 6x1/2(x2 + x) - 8x3/4 - 8x1/2 x?:O

In Problems 89-98, expressions that occur in calculus are given. Factor each expression. Express your answer so that only positive exponents occur. 6x1/2(2x + 3) + x3/2. 8

In Problems 89-98, expressions that occur in calculus are given. Factor each expression. Express your answer so that only positive exponents occur. 3(x2 + 4)4/3 + x 4 (x2+4)1/3 + 2x

In Problems 89-98, expressions that occur in calculus are given. Factor each expression. Express your answer so that only positive exponents occur. 2x(3x + 4)413 + x2. 4(3x + 4) 1/3

In Problems 89-98, expressions that occur in calculus are given. Factor each expression. Express your answer so that only positive exponents occur. 3 .. 4(3x + 5)1/3(2x + 3)3/2 + 3(3x + 5)4/3(2x + 3)1/2 "r>-2

In Problems 89-98, expressions that occur in calculus are given. Factor each expression. Express your answer so that only positive exponents occur. 6(6x + 1)1/3(4x - 3)3/2 + 6(6x + 1)4/3(4x - 3)1/2 r>- -4

In Problems 89-98, expressions that occur in calculus are given. Factor each expression. Express your answer so that only positive exponents occur. 3x-1/2 + 3x1/2 x>O

In Problems 89-98, expressions that occur in calculus are given. Factor each expression. Express your answer so that only positive exponents occur. 8xl/3 - 4x-2/3 x '1-0

In Problems 99-106, use a calculator to approximate each radical. Round your answer to two decimal places. V2

In Problems 99-106, use a calculator to approximate each radical. Round your answer to two decimal places. V7

In Problems 99-106, use a calculator to approximate each radical. Round your answer to two decimal places. 3V4

In Problems 99-106, use a calculator to approximate each radical. Round your answer to two decimal places. v-5

In Problems 99-106, use a calculator to approximate each radical. Round your answer to two decimal places. 2 + \13 3 - V

In Problems 99-106, use a calculator to approximate each radical. Round your answer to two decimal places. Vs - 2 V2 + 4

In Problems 99-106, use a calculator to approximate each radical. Round your answer to two decimal places. 3Vs - V2 --=--- \13

In Problems 99-106, use a calculator to approximate each radical. Round your answer to two decimal places. 2\13 - V4 V2

Calculating the Amount of Gasoline in a Tank A Shell station stores its gasoline in underground tanks that are right circular r cylinders lying on their sides. See the illustration. The volume V of gasoline in the tank (in gallons) is given by the formula V = 40h2 ): - 0.608 where h is the height of the gasoline (in inches) as measured on a depth stick. (a) If h = 12 inches, how many gallons of gasoline are in the tank? (b) If h = 1 inch, how many gallons of gasoline are in the tank?

Inclined Planes The final velocity v of an object in feet per second (ft/sec) after it slides down a frictionless inclined plane of height h feet is v = V64h + VB where Va is the initial velocity (in ft/sec) of the object. (a) What is the final velocity v of an object that slides down a frictionless inclined plane of height 4 feet? Assume that the initial velocity is O. (b) What is the final velocity v of an object that slides down a frictionless inclined plane of height 16 feet? Assume that the initial velocity is O. (c) What is the finaL-velocity v of an object that slides down a frictionless inclined plane of height 2 feet with an initial velocity of 4 ftlsec?

Problems 109-112 require the following information. '<:::""------' Period of a Pendulum The period T, in seconds, of a pendulum of length l, in feet, may be approximated using the formula T = 27r- In Problems 109-112, express your answer both as a square roo/ and as a decimal. Find the period T of a pendulum whose length is 64 feet.

Problems 109-112 require the following information. '<:::""------' Period of a Pendulum The period T, in seconds, of a pendulum of length l, in feet, may be approximated using the formula T = 27r- In Problems 109-112, express your answer both as a square roo/ and as a decimal. Find the period T of a pendulum whose length is 16 feet.

Problems 109-112 require the following information. '<:::""------' Period of a Pendulum The period T, in seconds, of a pendulum of length l, in feet, may be approximated using the formula T = 27r- In Problems 109-112, express your answer both as a square roo/ and as a decimal. Find the period T of a pendulum whose length is 8 inches.

Problems 109-112 require the following information. '<:::""------' Period of a Pendulum The period T, in seconds, of a pendulum of length l, in feet, may be approximated using the formula T = 27r- In Problems 109-112, express your answer both as a square roo/ and as a decimal. Find the period T of a pendulum whose length is 4 inches.

GiVe an example to show that W is not equal to a. Use it to explain why W = l al

In Problems 1-8, use U = universal set = {1, 2, 3, 4, 5, 6, 7, 8, 9 } , A = { I, 3, 5, 7 }, B = {3, 5, 6, 7, 8 }, and C = {2, 3, 7, 8, 9} to find each set. AUB

In Problems 1-8, use U = universal set = {1, 2, 3, 4, 5, 6, 7, 8, 9 } , A = { I, 3, 5, 7 }, B = {3, 5, 6, 7, 8 }, and C = {2, 3, 7, 8, 9} to find each set. BUe

In Problems 1-8, use U = universal set = {1, 2, 3, 4, 5, 6, 7, 8, 9 } , A = { I, 3, 5, 7 }, B = {3, 5, 6, 7, 8 }, and C = {2, 3, 7, 8, 9} to find each set. Ane

In Problems 1-8, use U = universal set = {1, 2, 3, 4, 5, 6, 7, 8, 9 } , A = { I, 3, 5, 7 }, B = {3, 5, 6, 7, 8 }, and C = {2, 3, 7, 8, 9} to find each set. AnB

In Problems 1-8, use U = universal set = {1, 2, 3, 4, 5, 6, 7, 8, 9 } , A = { I, 3, 5, 7 }, B = {3, 5, 6, 7, 8 }, and C = {2, 3, 7, 8, 9} to find each set. A

In Problems 1-8, use U = universal set = {1, 2, 3, 4, 5, 6, 7, 8, 9 } , A = { I, 3, 5, 7 }, B = {3, 5, 6, 7, 8 }, and C = {2, 3, 7, 8, 9} to find each set. B

In Problems 1-8, use U = universal set = {1, 2, 3, 4, 5, 6, 7, 8, 9 } , A = { I, 3, 5, 7 }, B = {3, 5, 6, 7, 8 }, and C = {2, 3, 7, 8, 9} to find each set. Bne

In Problems 1-8, use U = universal set = {1, 2, 3, 4, 5, 6, 7, 8, 9 } , A = { I, 3, 5, 7 }, B = {3, 5, 6, 7, 8 }, and C = {2, 3, 7, 8, 9} to find each set. AUB

In Problems 9 and 10, list the numbers in the set that are (a) Natural numbers, (b) Integers, (c) Rational numbers, (d) Irrational numbers, (e) Real numbers. A = { -10, 0.65,1.343434 ... , V7, }

In Problems 9 and 10, list the numbers in the set that are (a) Natural numbers, (b) Integers, (c) Rational numbers, (d) Irrational numbers, (e) Real numbers. B = { 0, -5, ,0.59, 1.333 ... , 2V2, }

In Problems 11-16, evaluate each expression. -6+4'(8 - 3)

In Problems 11-16, evaluate each expression. 5 1 18 + 12

In Problems 11-16, evaluate each expression. 4 9 3 16

In Problems 11-16, evaluate each expression. 5 11 27

In Problems 11-16, evaluate each expression. v3 -2

In Problems 11-16, evaluate each expression. (-3)5

In Problems 17 and 18, use the Distributive Property to remove the parentheses. 4(x - 3)

In Problems 17 and 18, use the Distributive Property to remove the parentheses. (x - 2)(3x + 1)

In Problems 19 and 20, graph the numbers x on the real number line. x > 3

In Problems 19 and 20, graph the numbers x on the real number line. x :s; 5

In Problems 21 and 22, let P, Q, and R be points on a real number line with coordinates -2,3, and 9, respectively. Find the distance between P and Q.

In Problems 21 and 22, let P, Q, and R be points on a real number line with coordinates -2,3, and 9, respectively. Find the distance between Q and R.

In Problems 23-28, evaluate each expression if x = -5 and y = 7. ""'- x + Y

In Problems 23-28, evaluate each expression if x = -5 and y = 7. 12x - 3yl

In Problems 23-28, evaluate each expression if x = -5 and y = 7. 5x1Y2

In Problems 23-28, evaluate each expression if x = -5 and y = 7. 2x2y-2

In Problems 23-28, evaluate each expression if x = -5 and y = 7. V2

In Problems 23-28, evaluate each expression if x = -5 and y = 7. Vx3

In Problems 29 and 30, determine the domain of the variable. 3 R-x - 6

In Problems 29 and 30, determine the domain of the variable. x + 1 -x + 5

In Problems 31 and 32, the triangles are similal: Find the missing length x and the missing angles A, B, and C.

In Problems 31 and 32, the triangles are similal: Find the missing length x and the missing angles A, B, and C.

Use a calculator to evaluate (1.5)4.

Identify the coefficient and degree of the monomial -5x3.

Identify the coefficients and degree of the polynomial \ 3x5 + 4X4 - 2x3 + 5x - 12.

Write 3.275 X lOs as an integer.

In Problems 37-44, perform the indicated operation. (2x4 - 8x3 + 5x - 1) + (6x3 + x2 + 4)

In Problems 37-44, perform the indicated operation. (x3 + 8x2 - 3x + 4) - (4x3 - 7x2 - 2x + 3)

In Problems 37-44, perform the indicated operation. (2x + y)(3x - 5y)

In Problems 37-44, perform the indicated operation. (2x - 5y)(3x + 2y)

In Problems 37-44, perform the indicated operation. (4x + 1)(4x - 1)

In Problems 37-44, perform the indicated operation. (5x + 2)2

In Problems 37-44, perform the indicated operation. (x + 1)(x + 2)(x - 3)

In Problems 37-44, perform the indicated operation. (x + 1)(x + 3)(x - 5)

In Problems 45-50, find the quotient and remainder. Check your work by verifying that (Quotient)(Divisor) + Remainder = Dividend 3x3 - x2 + X + 4 divided by x - 3

In Problems 45-50, find the quotient and remainder. Check your work by verifying that (Quotient)(Divisor) + Remainder = Dividend 2x3 - 3x2 + X + 1 divided by x - 2