1. Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 7.1 - 1 Greatest Common Factors; Factoring by Grouping

2. Copyright © 2010 Pearson Education, Inc. All rights reserved. Factoring 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 GCD is a factor of all the terms of the polynomial.

3. Copyright © 2010 Pearson Education, Inc. All rights reserved. Factoring Out the Greatest Common Factor

4. Copyright © 2010 Pearson Education, Inc. All rights reserved. Factoring Out a Binomial Factor The greatest common factor need not be a monomial.

5. Copyright © 2010 Pearson Education, Inc. All rights reserved. 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.

6. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 7.1 - 6 6.1 Greatest Common Factors; Factoring by Grouping Factoring by Grouping 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:

7. Copyright © 2010 Pearson Education, Inc. All rights reserved. Factoring by Grouping.

8. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 7.1 - 8 Factoring by Grouping

9. Copyright © 2010 Pearson Education, Inc. All rights reserved. Factoring by Grouping