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

2. 6.5 Lecture Guide: Factoring by Grouping and a General Strategy for Factoring Polynomials Objective: Factor polynomials by the method of grouping. Objective: Determine the most appropriate technique for factoring a polynomial.

3. Strategy for Factoring a Polynomial Over the Integers After factoring out the GCF (greatest common factor), proceed as follows. Binomials: Factor special forms: Difference of Two Squares Difference of Two Cubes Sum of Two Cubes is prime The sum of two squares is prime if x 2 and y 2 are only second-degree terms and have no common factor other than 1.

4. Strategy for Factoring a Polynomial Over the Integers Trinomials: Factor the forms that are perfect squares: Perfect Square Trinomial; a Square of a Sum Perfect Square Trinomial; a Square of a Difference Otherwise, factor the trinomial by the grouping method. Polynomials of Four or More Terms : Factor by grouping Your goal upon finishing this section is to be able to use the various methods to factor each given polynomial without being told which type it is.

5. Completely factor the following polynomials. 1.

6. Completely factor the following polynomials. 2.

7. Completely factor the following polynomials. 3.

8. Completely factor the following polynomials. 4.

9. Completely factor the following polynomials. 5.

10. Completely factor the following polynomials. 6.

11. Completely factor the following polynomials. 7.

12. Completely factor the following polynomials. 8.

13. Completely factor the following polynomials. 9.

14. Completely factor the following polynomials. 10.

15. Completely factor the following polynomials. 11.

16. Completely factor the following polynomials. 12.

17. Completely factor the following polynomials. 13.

18. Completely factor the following polynomials. 14.

19. Completely factor the following polynomials. 15.

20. Completely factor the following polynomials. 16.

21. Completely factor the following polynomials. 17.

22. Completely factor the following polynomials. 18.

23. Completely factor the following polynomials. 19.

24. Completely factor the following polynomials. 20.