1. Factoring Review EQ: How do I factor polynomials?

2. Ex. 1) Factor x 2 – 25 This is a “Difference of Two Squares” “difference” means subtraction ALWAYS CHECK FOR A GCF FIRST! (x + 5)(x – 5) FOIL to confirm!

3. Ex. 2) Factor 4a 2 – 25b 2 Are both of these terms perfect squares? Is there a minus sign in the middle? Then use “difference of squares”. (2a + 5b)(2a – 5b) FOIL to confirm!

4. Ex. 3) Factor 9x 2 – 15 Are both of these perfect squares? NO 15 is not. So, you can’t factor it using difference of squares… BUT you can factor using GCF. 3(3x 2 – 5)

5. Ex. 4) Factor 16r 2 + 49 Are both terms perfect squares? Yes Is there a minus sign in the middle? NO! Can’t factor using difference of squares. Is there a GCF? NO …. Must be PRIME

6. Ex. 5) Factor 25n 2 – 100 What should you always ask yourself FIRST??? GCF 25 (n 2 – 4) 25(n + 2)(n – 2) If you forgot, (5n + 10)(5n – 10)... Both of these factors are not factored COMPLETELY b/c they still have a common factor of 5 (each)! MUST DO GCF FIRST!!!!!!!!!!!!

7. Ex. 6-7: Practice Factor Completely! Ex. 6) X 2 – 4 Ex. 7) 36a 2 – 49b 2 6. (x + 2)(x – 2) 7. (6a + 7b)(6a – 7b)

8. Perfect Square Trinomial x²+bx+c What multiplies to give you “c” and adds to give you “b”? Your answer is a binomial squared

9. Ex. 8) Factor x 2 + 20x +100 (x + 10)(x + 10) When both factors are the same, this is called a PERFECT SQUARE TRINOMIAL and could be written……. (x + 10) 2

10. Ex. 9) Factor completely. x 2 + 6x + 8 When factoring, always make sure your polynomial is in standard form & always look for a GCF 1 st. Definition: leading coefficient – Coefficient on the term with the highest degree in a polynomial. If written in standard form, it will lead out the problem. What multiplies to give you 8 AND adds to give you 6? Answer: (x + 4) (x + 2) Check yourself by FOIL.

11. Lets change the sign of the middle term Example 10: x 2 – 6x + 8 (x – 2)(x – 4) Check by FOIL.

12. Ex. 11) Factor Completely x 2 + 14x + 40 (x + 10)(x + 4) FOIL to check.

13. Ex. 12) Factor Completely x 2 – 10x + 16 (x - 8 )(x - 2) FOIL to check

14. Ex. 13) Factor 2x 2 –18x + 40 What do you do first? Don’t forget you can ALWAYS use GCF first! 2(x – 4)(x – 5) FOIL, then distribute the 2 to check yourself!

15. Ex. 14) Factor x 2 + 2x - 8 What multiplies to give you -8, and adds to be 2? 4, -2 Which number goes where…. ? (x + 4)(x – 2) FOIL to check!

16. Ex. 15) x 2 – 2x - 8 (x + 2 )(x - 4) Foil to check!!!

17. Ex. 16) 2x 2 + 8x - 42 2(x + 7)(x - 3) FOIL TO CHECK!

18. Ex 17) Factor: 3x 3 +27x 2 + 42x 3x(x + 2)(x + 7) FOIL, then distribute 3x to check.

19. Ex 18) Factor 2x 2 + 11x – 21 Is there a GCF? NO! (2x – 3) (x + 7)

20. Ex 19) Factor 12x 2 + x – 20 Is there a GCF? No!!!!!!!!! (4x – 5)(3x + 4) FOIL to check.

21. Ex 20) Factor 3x 2 +5x - 28 Is there a GCF? NO! (3x – 7) (x + 4) FOIL to confirm.

22. Ex. 21) Factor 3x 2 – x - 6 Prime!!!!

23. Homework Page 295-296 4-6, 10-18, 22-25, 30-35, 38-39 Just 24 problems

24. Do Now: Factor the following: 1.x² - 36 2.9x² - 64 3.x² - 18x + 81 4.x² + 7x + 10 5.3x² + 16x + 16 6.4x² - 32x + 64

25. Homework Answers: 4. 2x(x-4) 5. 2y(y-3) 6. 5ax(x-3a) 10. (x+3)(x+2) 11. (x+7)(x+1) 12. (y-4)(y-1) 13. (x+2)(x-6) 14. (y+3)(y-12) 15. (x+12)(x-2) 16. (2x+5)(x+2) 17. (3x+2)(x+1) 18. (5x-2)(x+3) 22. (x²+9)(x+3)(x-3) 23. 2(x+2)(x-2) 24. (4x+5)(4x-5) 25. (x+4)² 30. 3(x+2) 31. 3(x²+6)

26. Continued… 32. n(10-n) 33. x(1-4x) 34. 2x(3-x) 35. -3y(y+5) OR 3y(-y-5) 38. ax(a+5ax-2) 39. 2ab(2b-3a)

27. Assignment Pg. 296, #’s40-57 ALL #46 – REWRITE IT: x²-22x-48 #48 – Rewrite in standard form #’s 49-51 – Rewrite, then factor out a negative: -x²+10x+56 becomes –(x²-10x-56)

28. Pg. 296, 40-57 40.(x-15)(x-1) 41. (x+4)² 42. (x-24)(x-2) 43. (x+8)(x-4) 44. (x+10)(x-3) 45. (x-12)(x+2) 46. (x-24)(x+2) 47. (x+6)(x-4) 48. (x+4)(x-14) 49. –(x+4)(x-14) 50. –(x+5)(x-6) 51. –(x+2)(x-12) 52. (3x+1)(x+3) 53. (2x+1)(x+2) 54. (2x+1)(x+1) 55. (3x+1)(x+2) 56. 3(4x+3)(x-1) 57. (3x+1)(x-2)