1. Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Sec 7.1 - 1 5.4 Greatest Common Factors; Factoring by Grouping

2. Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Sec 7.1 - 2 5.4 Greatest Common Factors; Factoring by Grouping Objectives 1.Factor out the greatest common factor. 2.Factor by grouping.

3. Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Sec 7.1 - 3 5.4 Greatest Common Factors; Factoring by Grouping Factor Out the Greatest Common Factor Both processes use the distributive property. Multiplying “undoes” factoring, and factoring “undoes” multiplying.

4. Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Sec 7.1 - 4 5.4 Greatest Common Factors; Factoring by Grouping Factor Out the Greatest Common Factor The first step in factoring is to find the greatest common factor (GCF) – the largest term that divides each term of the polynomial. The GCF is a factor of all the terms of the polynomial.

5. Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Sec 7.1 - 5 Factor Out the Greatest Common Factor

6. Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Sec 7.1 - 6 Factoring Out a Negative Common Factor When the coefficient of the term of greatest degree is negative, it is sometimes preferable to factor out the –1 that is understood along with the GCF. Factor only the 3 out. Or factor the – 3 out. Either is correct.

7. Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Sec 7.1 - 7 5.4 Greatest Common Factors; Factoring by Grouping Factoring Out a Binomial Factor The greatest common factor need not be a monomial. Think of this as two terms with a common factor of (a + b). Think of this as two terms with a common factor of a(b – c) 2.

8. Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Sec 7.1 - 8 5.4 Greatest Common Factors; Factoring by Grouping Factoring by Grouping Example 1 Many polynomials have no greatest common factor other than the number 1. Some of these can be factored using the distributive property if those terms with a common factor are grouped together. Consider the polynomial: 1.The first two terms have a 5 in common, whereas, 2.The last two terms have an x in common. Applying the distributive property, we have

9. Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Sec 7.1 - 9 5.4 Greatest Common Factors; Factoring by Grouping Factoring by Grouping This last expression can be thought of as having two terms, Applying the distributive property again to factor (x + y) from each term: and.

10. Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Sec 7.1 - 10 5.4 Greatest Common Factors; Factoring by Grouping Factoring by Grouping- 4 terms..

11. Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Sec 7.1 - 11 Factoring by Grouping Example 2 In order to factor a four term polynomial, we identify a common binomial factor by regrouping the polynomial into two groups of two terms each.

12. Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Sec 7.1 - 12 Homework Two Worksheets on Factoring out GCF and Grouping.