Developmental Algebra I Lab
Developmental Algebra I Lab MAT 095
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Dr. Karelle Keeling
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This 16 page Class Notes was uploaded by Dr. Karelle Keeling on Sunday October 11, 2015. The Class Notes belongs to MAT 095 at Eastern Kentucky University taught by Patrick Coen in Fall. Since its upload, it has received 11 views. For similar materials see /class/221453/mat-095-eastern-kentucky-university in Mat Mathematics at Eastern Kentucky University.
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Date Created: 10/11/15
Chapter 4 Exponents and Polynomials Section 41 Multiplication With Exponents Exponents and Bases 3x2 62 versus 732 Examples 52 73 Property 1 for Exponents lfa is any real number and rand 5 are integers then argtltasgt am 0 To multiply two expressions with the same base add exponents and use the common base Examples 7605 W3 KW Property 2 for Exponents lfa is any real number and rand 5 are integers then yr 2 am 0 A power raised to another power is the base raised to the product of powers Examples 54 3 X4 11 Property 3 for Exponents lfa and b are ant two real numbers and r is an integer then 1k 7 51 7 0 The power of a product is the product of powers Examples 4Y72 3X2Y85 SXZVQXSV Volume ofa Rectangular Solid VLWH Scienti c Notation A number is written in scienti c notation when it is written as the product ofa number between 1 and 10 and an integer power of 10 A number written in scienti c notation has the form 71 X107 where 1 S 71 lt10 and ran integer To write a number in scienti c notation 1 Move the decimal point until the value of the number is between 1 and 10 Count the spaces as you move 2 Ifyou moved right the count is negative You started with a small number 3 Ifyou moved left the count is positive You started with a large number Write the new number step one times 10 to the count step 2 or 3 To write a number in standard notation 1 If the exponent on 10 is positive move the decimal point that number of spaces to the right You will have a large number for your solution 2 If the exponent on 10 is negative move the decimal point that number of spaces to the left You will have a small number for your solution Examples Write in scienti c notation 1 763000 2 000000328 Write in standard notation 1 285 gtlt107 2 246 gtlt10 8 Section 42 Division with Exponents Negative Exponents lfa is a real number other than 0 and r is a positive integer then 1 Examples 3 2 4 3 2965 Property 4 for Exponents lfa is a nonzero real number and r and s are integers then a 77 i a r a 0 To divide the same base subtract the exponent in the denominator from the exponent in the numerator and raise the base to the exponent that results Examples X7 315 Property 5 for Exponents lfa and b are any two real numbers b i 0 and r is an integer then Zero Exponent Rule If a does not equal zero then a01 Exmples 3 3a 1 7 Summary of Exponent Properties H21 and b are real numbers and r and s are integers then De nitions air i 2101 21121 Section 43 Operations with Monomials De nition A monomial is a oneiterm expression that is either a constant number or the product ofa constant and one or more variables raised to Whole number exponents The numerical part of the monomial is called the coef cient Multiplying Monomials To multiply monomials we Z multiply coef cients Z multiply like variables Examples 1 73x55x2 1 2 3 4 2 X SXJ 3 2X8 5972 4Y5 Dividing Monomials To divide monomials we quot divide coef cients Z divide like variables Examples 48 9 1 E 6 Z 36x7 2 2X10 15551 3 45318 42x109 2x105 5 31x10 3X4x106 6 49632 996310 I 3963 2963 Adding and Subtracting Monomials De nition Two terms monomials with the same variable part variable and exponent are called similar or like terms 0 When adding or subtracting monomials combine the coef cient and keep the variable part the 821116 Using the Distributive Property 3X24X2 Examples 1 106 7 156 2 713Xy2 7 3Xy2 3 5X2 8x3 1659 28a 4 7 7 4a 4a4 Section 44 Addition and Subtraction of Polynomials De nition A polynomial is the sum ofmonomials De nition The degree ofa polynomial in one variable is the highest power ofwhich the variable is raised Adding Polynomials Examples 1 12x57 3X29X5 75x3x 7 8 2 3X2yxy277 74Xy23 Subtracting Polynomials Change to adding the opposite Examples 1 12x373X29X5 7 75x3x 7 8 2 Subtract 8a24ab7b2 from 3a26ab3b2 Section 45 Multiplication with Polynomials Multiply 2X2y5 75X4y Multiply 76X5lt2Xy 7 3Xy2 Multiplying Binomials 3 Methods Z Distributive Property Z FOIL Method only with two binomials Z Column Method 2X3X 7 5 Examples 1 3X 7 2X4 2 X42X2 7 3X 1 3 3X 7 22X24X 7 5 4 The length ofa rectangle is 2 less than 3 times the Width Find an expression for the area Section 46 Binomial Squares and Other Special Products Square ofa binomial x52 x 7 52 ab2a22abb2 aib2a272abb2 Difference of Squares x 5x 5 21 b aib a2 7b2 WARNING 2mg2 2 a2b2 Use these rules to multiply the following 1 x 42 2 2x 7 5y 3 3X 77gtlt3X 7 Section 47 Dividing a Polynomial by a Monomial To divide a polynomial by a monomial just divide each term in the polynomial by the monomial Examples 1 75966 50963 25X I 5X 2 4M5 16a2k2 22 39 2ak 3 16x5 8x2 4x I 4X 7d2X l4dX2 21d2X2 4 2 2 2851 X 5 5X26X 36X33X l 3X Section 31 Paired Data and Graphing Ordered Pairs Scatter Diagrams and Line Graphs Make a scatter diagram and line chart of the information AGE 9 11 HEIGHT 51 57 Rectangular Coordinate System Cartesian Concepts XeaXiS horizontal yiaxis vertical Origin Quadrants Ordered pairs PX y Xicoordinate and yicoordinate Graph the following ordered pairs 1 3 5 2 7 3 3 4 2 4 1 5 5 6 0 6 0 3 64 72 EXaInple Graph the points 4 3 and 74 71 and draw a straight line that passes through both of them Does 72 0 lie on the line Does 76 2 lie on the line Section 32 Solutions to Linear Equations in Two Variables Equations with 2 variables will have both X and y Solutions to linear equations are ordered pairs X y that satisfy the equation Example Find three solutions that satisfy the equation X y 7 Graph the solutions Using the equation X2y10 complete the ordered pairs below 3 s We could Write this in table form Complete the table above for the equation X2y10 Which of the ordered pairs below are solutions to 73X SyZSOP o 6 710 1 5 3 The phone company charges 2 per long distance call plus 025 per minute Write an equation for the cost of a call in terms ofminutes used Section 33 Graphing Linear Equations AXByZC is called Standard Form of a Line when A B and C are real numbers and both A and B are not zero To graph a linear equation in 2 variables 1 Find any three points that satisfy the equation 2 Graph the points 3 Connect the points with a line 1 Graph the solution set for X y 8 2 Graph the solution set for y 2X 71 1 3 Graph the solution set for y EX 3
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