1. Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Section 6.1 Removing a Common Factor

2. 2 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Common Factors When two or more numbers, variables, or algebraic expressions are multiplied, each is called a 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. 15xy = 3 · 5 · x · y 5 · 3 Factor 5x 2 · 3y 4 Factor

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

4. 4 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Example Factor. 12xy + 6xz 12xy + 6xz 2 is also a factor of 12 and 6, but 6 is the greatest common factor.

5. 5 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. 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?” 3. 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. Factoring a Polynomial With Common Factors

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

7. 7 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Example Factor. The GCF is 8x 2 y

8. 8 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Example Factor. The GCF is 9a 2 b 2

9. 9 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Example Factor. 6(3x + y) – z(3x + y) The common factor is 3x + y. 6(3x + y) – z(3x + y)

10. 10 Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Example Factor. The common factor is 2x – 3y.