1. Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 6.6 - 1

2. Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 6.6 - 2 Factoring and Applications Chapter 6

3. Copyright © 2010 Pearson Education, Inc. All rights reserved Sec 6.6 - 3 6.6 A General Approach to Factoring

4. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.6 - 4 6.6 A General Approach to Factoring Objectives 1.Factor out any common factor. 2.Factor binomials. 3.Factor trinomials. 4.Factor polynomials with more than three terms.

5. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.6 - 5 6.6 A General Approach to Factoring Factoring a Polynomial A polynomial is completely factored when 1)it is written as a product of prime polynomials with integer coefficients, and 2)none of the of polynomial factors can be factored further.

6. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.6 - 6 6.6 A General Approach to Factoring Factoring Out a Common Factor This step is always the same, regardless of the number of terms in the polynomial. Factor each polynomial. (a) (b) (c)

7. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.6 - 7 6.6 A General Approach to Factoring Factoring Binomials

8. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.6 - 8 6.6 A General Approach to Factoring Factoring Binomials Use one of the rules to factor each binomial if possible. (a) (b)

9. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.6 - 9 6.6 A General Approach to Factoring Factoring Binomials Use one of the rules to factor each binomial if possible. (c) (d) is prime. It is the sum of squares. Sum of cubes The binomial 25m 2 + 625 is the sum of squares. It can be factored, however as 25(m 2 + 25) because it has a common factor, 25.

10. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.6 - 10 6.6 A General Approach to Factoring Factoring Trinomials

11. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.6 - 11 6.6 A General Approach to Factoring Factoring Trinomials Factor each trinomial. (a) (b) (c) The numbers -6 and 1 have a product of -6 and a sum of -5.

12. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.6 - 12 6.6 A General Approach to Factoring Factoring Trinomials Factor each trinomial. (d) (e)

13. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.6 - 13 6.6 A General Approach to Factoring Factoring Polynomials with More than Three Terms Factor each polynomial. Consider factoring by grouping. (a) (b) Group the terms. Factor each group. 5k + 1 is a common factor. Difference of squares Group the first three terms. Perfect square trinomial Difference of squares

14. Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 6.6 - 14 6.6 A General Approach to Factoring Factoring Polynomials with More than Three Terms Factor each polynomial. Consider factoring by grouping. (a) Rearrange and group the terms. Factor each group. Factor out 2m – n.