1. Section 6.5 Factoring by Grouping and a General Strategy for Factoring Polynomials

2. Objective 1: Factor polynomials by the method of grouping. Your goal upon finishing this section is to be able to use the various methods covered in this chapter to factor each given polynomial. In this first set of problems it is necessary to group pairs of terms as was done in Section 6.1. It may be necessary to reorder the terms to find a useful grouping. 6.5 Lecture Guide: Factoring by Grouping and a General Strategy for Factoring Polynomials

3. Completely factor the following polynomials. 1.

4. Completely factor the following polynomials. 2.

5. 3. Completely factor the following polynomials.

6. 4. Completely factor the following polynomials.

7. 5. Factor each polynomial by using the special pattern.

8. 6. Factor each polynomial by using the special pattern.

9. Sometimes it is necessary to group 3 terms together. Start by trying to pick out a perfect square trinomial. 7.

10. Sometimes it is necessary to group 3 terms together. Start by trying to pick out a perfect square trinomial. 8.

11. Objective 2: Determine the most appropriate method for factoring a polynomial.

12. After factoring out the GCF (greatest common factor), proceed as follows. Binomials: Factor special forms: _________ of Two Squares Difference of Two_______ _________ of Two Cubes is primeThe sum of two squares is____________ if and are only second-degree terms and have no common factor other than 1. Strategy for Factoring a Polynomial Over the Integers

13. After factoring out the GCF (greatest common factor), proceed as follows. Trinomials: Factor the forms that are perfect squares: Perfect Square Trinomial; a Square of a Sum Perfect Square Trinomial; a Square of a Difference Factor trinomials that are not perfect squares by inspection if possible; otherwise, use the trial-and-error method or the AC method. Polynomials of Four or More Terms: Factor by grouping

14. 9. Factor each polynomial completely. If it is prime write “Prime” and justify your answer.

15. 10. Factor each polynomial completely. If it is prime write “Prime” and justify your answer.

16. 11. Factor each polynomial completely. If it is prime write “Prime” and justify your answer.

17. 12. Factor each polynomial completely. If it is prime write “Prime” and justify your answer.

18. 13. Factor each polynomial completely. If it is prime write “Prime” and justify your answer.

19. 14. Factor each polynomial completely. If it is prime write “Prime” and justify your answer.

20. 15. Factor each polynomial completely. If it is prime write “Prime” and justify your answer.

21. 16. Factor each polynomial completely. If it is prime write “Prime” and justify your answer.

22. 17. Factor each polynomial completely. If it is prime write “Prime” and justify your answer.

23. 18. Factor each polynomial completely. If it is prime write “Prime” and justify your answer.

24. 19. Factor each polynomial completely. If it is prime write “Prime” and justify your answer.

25. 20. Factor each polynomial completely. If it is prime write “Prime” and justify your answer.