1. Copyright © 2010 Pearson Education, Inc. All rights reserved. 6.5 – Slide 1

2. Copyright © 2010 Pearson Education, Inc. All rights reserved. 6.5 – Slide 2 Factoring and Applications Chapter 6

3. Copyright © 2010 Pearson Education, Inc. All rights reserved. 6.5 – Slide 3 6.5 Special Factoring Techniques

4. Copyright © 2010 Pearson Education, Inc. All rights reserved. 6.5 – Slide 4 6.5 Special Factoring Techniques Objectives 1.Factor a difference of squares. 2.Factor a perfect square trinomial. 3.Factor a difference of cubes. 4.Factor a sum of cubes.

5. Copyright © 2010 Pearson Education, Inc. All rights reserved. 6.5 – Slide 5 Factor a difference of squares 6.5 Special Factoring Techniques

6. Copyright © 2010 Pearson Education, Inc. All rights reserved. 6.5 – Slide 6 6.5 Special Factoring Techniques Example 1 Factor each binomial, if possible. Factor a difference of squares (a) x 2  49 (b) y 2  m 2 = (y – m)(y + m) (continued)

7. Copyright © 2010 Pearson Education, Inc. All rights reserved. 6.5 – Slide 7 6.5 Special Factoring Techniques Example 1 Factor each binomial, if possible. Factor a difference of squares (d) x 2  8 (e) p 2 + 16 It is a prime polynomial because 8 is not the square of an integer. It is a prime polynomial since it is a sum of squares.

8. Copyright © 2010 Pearson Education, Inc. All rights reserved. 6.5 – Slide 8 6.5 Special Factoring Techniques Example 2 Factor each difference of squares. Factor a difference of squares

9. Copyright © 2010 Pearson Education, Inc. All rights reserved. 6.5 – Slide 9 6.5 Special Factoring Techniques Example 3 Factor completely. Factor a difference of squares

10. Copyright © 2010 Pearson Education, Inc. All rights reserved. 6.5 – Slide 10 6.5 Special Factoring Techniques Example 3 Factor completely. Factor a difference of squares

11. Copyright © 2010 Pearson Education, Inc. All rights reserved. 6.5 – Slide 11 Factor a perfect square trinomial. 6.5 Special Factoring Techniques

12. Copyright © 2010 Pearson Education, Inc. All rights reserved. 6.5 – Slide 12 6.5 Special Factoring Techniques Example 4 Factor x 2 + 10x + 25. Factor a perfect square trinomial. The term x 2 is a perfect square, and so is 25. Try factoring as (x + 5) 2. To check, take twice the product of the two terms in the squared binomial. Since 10x is the middle term of the trinomial, the trinomial is a perfect square and can be factored as (x + 5) 2.

13. Copyright © 2010 Pearson Education, Inc. All rights reserved. 6.5 – Slide 13 6.5 Special Factoring Techniques Example 5 Factor each trinomial. Factor a perfect square trinomial. (a) x 2 – 22x + 121 The first and last terms are perfect squares. Check to see if the middle term is twice the product of the first and last terms of the binomial x – 11.

14. Copyright © 2010 Pearson Education, Inc. All rights reserved. 6.5 – Slide 14 6.5 Special Factoring Techniques Example 5 Factor each trinomial. Factor a perfect square trinomial.

15. Copyright © 2010 Pearson Education, Inc. All rights reserved. 6.5 – Slide 15 6.5 Special Factoring Techniques Example 5 Factor each trinomial. Factor a perfect square trinomial. Twice the product of the first and last terms is 2(5y)4 = 40y, which is not the middle term. The trinomial is not a perfect square. It is a prime polynomial.

16. Copyright © 2010 Pearson Education, Inc. All rights reserved. 6.5 – Slide 16 6.5 Special Factoring Techniques Example 5 Factor each trinomial. Factor a perfect square trinomial.

17. Copyright © 2010 Pearson Education, Inc. All rights reserved. 6.5 – Slide 17 6.5 Special Factoring Techniques Factor a perfect square trinomial.

18. Copyright © 2010 Pearson Education, Inc. All rights reserved. 6.5 – Slide 18 6.5 Special Factoring Techniques Factor a difference of cubes.

19. Copyright © 2010 Pearson Education, Inc. All rights reserved. 6.5 – Slide 19 6.5 Special Factoring Techniques Example 6a Factor the difference of cubes. Factor a difference of cubes.

20. Copyright © 2010 Pearson Education, Inc. All rights reserved. 6.5 – Slide 20 6.5 Special Factoring Techniques Example 6c Factor the difference of cubes. Factor a difference of cubes.

21. Copyright © 2010 Pearson Education, Inc. All rights reserved. 6.5 – Slide 21 6.5 Special Factoring Techniques Factor a sum of cubes.

22. Copyright © 2010 Pearson Education, Inc. All rights reserved. 6.5 – Slide 22 6.5 Special Factoring Techniques Example 7a Factor the sum of cubes. Factor a sum of cubes.

23. Copyright © 2010 Pearson Education, Inc. All rights reserved. 6.5 – Slide 23 6.5 Special Factoring Techniques Example 7b Factor the sum of cubes. Factor a sum of cubes.

24. Copyright © 2010 Pearson Education, Inc. All rights reserved. 6.5 – Slide 24 6.5 Special Factoring Techniques Factor a sum of cubes.