1. 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objectives 2 Greatest Common Factors and Factoring by Grouping Factor out the greatest common factor. Factor by grouping. 6.1

2. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Writing a polynomial as the product of two or more simpler polynomials is called factoring the polynomial. 3x(5x – 2) = 15x 2 – 6xMultiplying 15x 2 – 6x = 3x(5x – 2)Factoring Factoring “undoes” or reverses, multiplying. Slide 6.1- 2 Greatest Common Factors and Factoring by Grouping

3. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Factor out the greatest common factor. Objective 1 Slide 6.1- 3

4. Copyright © 2012, 2008, 2004 Pearson Education, Inc. The first step in factoring a polynomial is to find the greatest common factor for the terms of the polynomial. The greatest common factor (GCF) is the largest term that is a factor of all terms in the polynomial. Slide 6.1- 4 Factor out the greatest common factor.

5. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Factor out the greatest common factor. Slide 6.1- 5 CLASSROOM EXAMPLE 1 Factoring Out the Greatest Common Factor 32m + 247k + 28 8a – 9 5z + 5

6. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Factor out the greatest common factor. Slide 6.1- 6 CLASSROOM EXAMPLE 2 Factoring Out the Greatest Common Factor 100m 5 – 50m 4 + 25m 3 5m 4 x 3 + 15m 5 x 6 – 20m 4 x 6

7. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Factor out the greatest common factor. Slide 6.1- 7 CLASSROOM EXAMPLE 3 Factoring Out a Binomial Factor (a + 2)(a – 3) + (a + 2)(a + 6) (y – 1)(y + 3) – (y – 1)(y + 4)

8. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Factor out the greatest common factor. Slide 6.1- 8 CLASSROOM EXAMPLE 3 Factoring Out a Binomial Factor (cont’d) k 2 (a + 5b) + m 2 (a + 5b) 2

9. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Factor in two ways. Slide 6.1- 9 CLASSROOM EXAMPLE 4 Factoring Out a Negative Common Factort –6r 2 + 5r

10. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Factoring by grouping. Objective 2 Slide 6.1- 10

11. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Sometimes individual terms of a polynomial have a greatest common factor of 1, but it still may be possible to factor the polynomial by using a process called factoring by grouping. We usually factor by grouping when a polynomial has more than three terms. Slide 6.1- 11 Factoring by grouping.

12. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Factoring by Grouping Step 1 Group terms. Collect the terms into groups so that each group has a common factor. Step 2 Factor within groups. Factor out the common factor in each group. Step 3 Factor the entire polynomial. If each group now has a common factor, factor it out. If not, try a different grouping. Always check the factored form by multiplying. Slide 6.1- 12 Factoring by grouping.

13. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Factor. Slide 6.1- 13 CLASSROOM EXAMPLE 5 Factoring by Grouping 6p – 6q + rp – rq. xy – 2y – 4x + 8.

14. Copyright © 2012, 2008, 2004 Pearson Education, Inc. Factor. Slide 6.1- 14 CLASSROOM EXAMPLE 7 Factoring by Grouping kn + mn – k – m 10x 2 y 2 – 18 + 15y 2 – 12x 2.