Section 6 1 Removing a Common Factor Copyright

Common Factors When two or more numbers, variables, or algebraic expressions are multiplied, each

Example Factor. 15 x – 5 = 5(x – 3) Find a factor both

Example Factor. 12 xy + 6 xz 2 is also a factor of 12

Factoring a Polynomial With Common Factors 1. Determine the greatest numerical common factor by

Example Factor. 36 a 6 + 45 a 4 – 18 a 2 9

Example Factor. The GCF is 8 x 2 y Copyright © 2012, 2009, 2005,

Example Factor. The GCF is 9 a 2 b 2 Copyright © 2012, 2009,

Example Factor. 6(3 x + y) – z(3 x + y) The common factor

Example Factor. The common factor is 2 x – 3 y. Copyright © 2012,

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Common Factors When two or more numbers, variables, or algebraic expressions are multiplied, each is called a factor. 5· 3 Factor 5 x 2 · 3 y 4 Factor When asked to factor a number or algebraic expression, you are being asked to determine what factors, when multiplied, will result in that number or expression. Factor. 15 xy = 3 · 5 · x · y Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. 2

Example Factor. 15 x – 5 = 5(x – 3) Find a factor both terms have in common. Rewrite the expression as a product. Check: 5(x – 3) = 15 x – 5 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. 3

Factoring a Polynomial With Common Factors 1. Determine the greatest numerical common factor by asking, “What is the largest integer that will divide into the coefficient of all the terms? ” 2. Determine the greatest common variable factor by asking, “What variables are common to all the terms? ” Then, for each variable that is common to all the terms, ask, “What is the largest exponent of the variable that is common to all the terms? ” The common factors found in steps 1 and 2 are the first part of the answer. 4. After removing the common factors, what remains is placed in parentheses as the second factor. 3. Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. 5

Example Factor. 36 a 6 + 45 a 4 – 18 a 2 9 a 2 is the common factor. Check: 9 a 2(4 a 4 + 5 a 2 – 2) = 36 a 6 + 45 a 4 – 18 a 2 Multiplying the factors yields the original polynomial. Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. 6