Recall that a graphing calculator may be used to check

Factor each trinomial. See Examples 1 through 4. x2 + 9x + 18

Factor each trinomial. See Examples 1 through 4. x2 + 9x + 20

Factor each trinomial. See Examples 1 through 4. x2 - 12x + 32

Factor each trinomial. See Examples 1 through 4. x2 - 12x + 27

Factor each trinomial. See Examples 1 through 4. x2 + 10x - 24

Factor each trinomial. See Examples 1 through 4. x2 + 3x - 54

Factor each trinomial. See Examples 1 through 4. x2 - 2x - 24

Factor each trinomial. See Examples 1 through 4. x2 - 9x - 36

Factor each trinomial. See Examples 1 through 4. 3x2 - 18x + 24

Factor each trinomial. See Examples 1 through 4. 5x2 - 45x + 70

Factor each trinomial. See Examples 1 through 4. 4x2 z + 28xz + 40z

Factor each trinomial. See Examples 1 through 4. x2 y2 + 4xy2 + 3y2

Factor each trinomial. See Examples 1 through 4. 2x2 - 24x - 64

Factor each trinomial. See Examples 1 through 4. 3n2 - 6n - 51

Factor each trinomial. See Examples 5 through 10. 5x2 + 16x + 3

Factor each trinomial. See Examples 5 through 10. 3x2 + 8x + 4

Factor each trinomial. See Examples 5 through 10. 2x2 - 11x + 12

Factor each trinomial. See Examples 5 through 10. 3x2 - 19x + 20

Factor each trinomial. See Examples 5 through 10. 2x2 + 25x - 20

Factor each trinomial. See Examples 5 through 10. 6x2 + 13x + 8

Factor each trinomial. See Examples 5 through 10. 4x2 - 12x + 9

Factor each trinomial. See Examples 5 through 10. 25x2 - 30x + 9

Factor each trinomial. See Examples 5 through 10. 12x2 + 10x - 50

Factor each trinomial. See Examples 5 through 10. 12y2 - 48y + 45

Factor each trinomial. See Examples 5 through 10. 3y4 - y3 - 10y2

Factor each trinomial. See Examples 5 through 10. 2x2 z + 5xz - 12z

Factor each trinomial. See Examples 5 through 10. 6x3 + 8x2 + 24x

Factor each trinomial. See Examples 5 through 10. 18y3 + 6y2 + 2y

Factor each trinomial. See Examples 5 through 10. 2x2 - 5xy - 3y2

Factor each trinomial. See Examples 5 through 10. 6x2 + 11xy + 4y2

Factor each trinomial. See Examples 5 through 10. 28y2 + 22y + 4

Factor each trinomial. See Examples 5 through 10. 24y3 - 2y2 - y

Factor each trinomial. See Examples 5 through 10. 2x2 + 15x - 27

Factor each trinomial. See Examples 5 through 10. 3x2 + 14x + 15

Use substitution to factor each polynomial completely. See Examples 11 and 12. x4 + x2 - 6

Use substitution to factor each polynomial completely. See Examples 11 and 12. x4 - x2 - 20

Use substitution to factor each polynomial completely. See Examples 11 and 12. 15x + 122 + 815x + 12 + 7

Use substitution to factor each polynomial completely. See Examples 11 and 12. 13x - 122 + 513x - 12 + 6

Use substitution to factor each polynomial completely. See Examples 11 and 12. x6 - 7x3 + 12

Use substitution to factor each polynomial completely. See Examples 11 and 12. x6 - 4x3 - 12

Use substitution to factor each polynomial completely. See Examples 11 and 12. 1a + 522 - 51a + 52 - 24

Use substitution to factor each polynomial completely. See Examples 11 and 12. 13c + 622 + 1213c + 62 - 28

Factor each polynomial completely. See Examples 1 through 12. x2 - 24x - 81

Factor each polynomial completely. See Examples 1 through 12. x2 - 48x - 100

Factor each polynomial completely. See Examples 1 through 12. x2 - 15x - 54

Factor each polynomial completely. See Examples 1 through 12. x2 - 15x + 54

Factor each polynomial completely. See Examples 1 through 12. 3x2 - 6x + 3

Factor each polynomial completely. See Examples 1 through 12. 8x2 - 8x + 2

Factor each polynomial completely. See Examples 1 through 12. 3x2 - 5x - 2

Factor each polynomial completely. See Examples 1 through 12. 5x2 - 14x - 3

Factor each polynomial completely. See Examples 1 through 12. 8x2 - 26x + 15

Factor each polynomial completely. See Examples 1 through 12. 12x2 - 17x + 6

Factor each polynomial completely. See Examples 1 through 12. 18x4 + 21x3 + 6x2

Factor each polynomial completely. See Examples 1 through 12. 20x5 + 54x4 + 10x3

Factor each polynomial completely. See Examples 1 through 12. x2 + 8xz + 7z2

Factor each polynomial completely. See Examples 1 through 12. a2 - 2ab - 15b2

Factor each polynomial completely. See Examples 1 through 12. x2 - x - 12

Factor each polynomial completely. See Examples 1 through 12. x2 + 4x - 5

Factor each polynomial completely. See Examples 1 through 12. 3a2 + 12ab + 12b2

Factor each polynomial completely. See Examples 1 through 12. 2x2 + 16xy + 32y2

Factor each polynomial completely. See Examples 1 through 12. x2 + 4x + 5

Factor each polynomial completely. See Examples 1 through 12. x2 + 5x + 8

Factor each polynomial completely. See Examples 1 through 12. 21x + 422 + 31x + 42 - 5

Factor each polynomial completely. See Examples 1 through 12. 31x + 322 + 21x + 32 - 5

Factor each polynomial completely. See Examples 1 through 12. 6x2 - 49x + 30

Factor each polynomial completely. See Examples 1 through 12. 4x2 - 39x + 27

Factor each polynomial completely. See Examples 1 through 12. x4 - 5x2 - 6

Factor each polynomial completely. See Examples 1 through 12. x4 - 5x2 + 6

Factor each polynomial completely. See Examples 1 through 12. 6x3 - x2 - x

Factor each polynomial completely. See Examples 1 through 12. 12x3 + x2 - x

Factor each polynomial completely. See Examples 1 through 12. 12a2 - 29ab + 15b2

Factor each polynomial completely. See Examples 1 through 12. 16y2 + 6yx - 27x2

Factor each polynomial completely. See Examples 1 through 12. 9x2 + 30x + 25

Factor each polynomial completely. See Examples 1 through 12. 4x2 + 12x + 9

Factor each polynomial completely. See Examples 1 through 12. 3x2 y - 11xy + 8y

Factor each polynomial completely. See Examples 1 through 12. 5xy2 - 9xy + 4x

Factor each polynomial completely. See Examples 1 through 12. 2x2 + 2x - 12

Factor each polynomial completely. See Examples 1 through 12. 3x2 + 6x - 45

Factor each polynomial completely. See Examples 1 through 12. 1x - 422 + 31x - 42 - 18

Factor each polynomial completely. See Examples 1 through 12. 1x - 322 - 21x - 32 - 8

Factor each polynomial completely. See Examples 1 through 12. 2x6 + 3x3 - 9

Factor each polynomial completely. See Examples 1 through 12. 3x6 - 14x3 + 8

Factor each polynomial completely. See Examples 1 through 12. 72xy4 - 24xy2 z + 2xz2

Factor each polynomial completely. See Examples 1 through 12. 36xy2 - 48xyz2 + 16xz4

Factor each polynomial completely. See Examples 1 through 12. 2x3 y + 2x2 y - 12xy

Factor each polynomial completely. See Examples 1 through 12. 3x2 y3 + 6x2 y2 - 45x2 y

Factor each polynomial completely. See Examples 1 through 12. x2 + 6xy + 5y2

Factor each polynomial completely. See Examples 1 through 12. x2 + 6xy + 8y2

Multiply. See Section 5.4. 1x - 321x + 32

Multiply. See Section 5.4. 1x - 421x + 42

Multiply. See Section 5.4. 12x + 122

Multiply. See Section 5.4. 13x + 522

Multiply. See Section 5.4. 1x - 221x2 + 2x + 42

Multiply. See Section 5.4. 1y + 121y2 - y + 12

Find all positive and negative integers b such that x2 + bx + 6 is factorable

Find all positive and negative integers b such that x2 + bx - 10 is factorable.

The volume V1x2 of a box in terms of its height x is given by the function V1x2 = x3 + 2x2 - 8x. Factor this expression for V1x2.

Based on your results from Exercise 97, find the length and width of the box if the height is 5 inches and the dimensions of the box are whole numbers.

Suppose that a movie is being filmed in New York City. An action shot requires an object to be thrown upward with an initial velocity of 80 feet per second off the top of 1 Madison Square Plaza, a height of 576 feet. The height h1t2 in feet of the object after t seconds is given by the function h1t2 = -16t 2 + 80t + 576. (Source: The World Almanac) a. Find the height of the object at t = 0 seconds, t = 2 seconds, t = 4 seconds, and t = 6 seconds. b. Explain why the height of the object increases and then decreases as time passes. c. Factor the polynomial -16t 2 + 80t + 576.

Suppose that an object is thrown upward with an initial velocity of 64 feet per second off the edge of a 960-foot cliff. The height h1t2 in feet of the object after t seconds is given by the function h1t2 = -16t 2 + 64t + 960 a. Find the height of the object at t = 0 seconds, t = 3 seconds, t = 6 seconds, and t = 9 seconds. b. Explain why the height of the object increases and then decreases as time passes. c. Factor the polynomial -16t 2 + 64t + 960.

Factor. Assume that variables used as exponents represent positive integers x2n + 10xn + 16

Factor. Assume that variables used as exponents represent positive integers x2n - 7xn + 12

Factor. Assume that variables used as exponents represent positive integers x2n - 3xn - 18

Factor. Assume that variables used as exponents represent positive integers x2n + 7xn - 18

Factor. Assume that variables used as exponents represent positive integers 2x2n + 11xn + 5

Factor. Assume that variables used as exponents represent positive integers 3x2n - 8xn + 4

Factor. Assume that variables used as exponents represent positive integers 4x2n - 12xn + 9

Factor. Assume that variables used as exponents represent positive integers 9x2n + 24xn + 16

Recall that a graphing calculator may be used to check addition, subtraction, and multiplication of polynomials. In the same manner, a graphing calculator may be used to check factoring of polynomials in one variable. For example, to see that 2x3 - 9x2 - 5x = x12x + 121x - 52 graph Y1 = 2x3 - 9x2 - 5x and Y2 = x12x + 121x - 52. Then trace along both graphs to see that they coincide. Factor the following and use this method to check your results. x4 + 6x3 + 5x2

Recall that a graphing calculator may be used to check addition, subtraction, and multiplication of polynomials. In the same manner, a graphing calculator may be used to check factoring of polynomials in one variable. For example, to see that 2x3 - 9x2 - 5x = x12x + 121x - 52 graph Y1 = 2x3 - 9x2 - 5x and Y2 = x12x + 121x - 52. Then trace along both graphs to see that they coincide. Factor the following and use this method to check your results. x3 + 6x2 + 8x

Recall that a graphing calculator may be used to check addition, subtraction, and multiplication of polynomials. In the same manner, a graphing calculator may be used to check factoring of polynomials in one variable. For example, to see that 2x3 - 9x2 - 5x = x12x + 121x - 52 graph Y1 = 2x3 - 9x2 - 5x and Y2 = x12x + 121x - 52. Then trace along both graphs to see that they coincide. Factor the following and use this method to check your results. 30x3 + 9x2 - 3x

Recall that a graphing calculator may be used to check addition, subtraction, and multiplication of polynomials. In the same manner, a graphing calculator may be used to check factoring of polynomials in one variable. For example, to see that 2x3 - 9x2 - 5x = x12x + 121x - 52 graph Y1 = 2x3 - 9x2 - 5x and Y2 = x12x + 121x - 52. Then trace along both graphs to see that they coincide. Factor the following and use this method to check your results. -6x4 + 10x3 - 4x2