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Factoring Review

Factoring Review. EQ: How do I factor polynomials?. 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!. Ex. 2) Factor 4a 2 – 25b 2.

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Factoring Review

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

  2. Ex. 1) Factor x2 – 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 4a2 – 25b2 • 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 9x2 – 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(3x2 – 5)

  5. Ex. 4) Factor 16r2 + 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 25n2 – 100 • What should you always ask yourself FIRST??? • GCF • 25 (n2 – 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) X2 – 4 Ex. 7) 36a2 – 49b2 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 • x2 + 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. • x2 + 6x + 8 • When factoring, always make sure your polynomial is in standard form & always look for a GCF 1st. • 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: • x2 – 6x + 8 • (x – 2)(x – 4) • Check by FOIL.

  12. Ex. 11) Factor Completely • x2 + 14x + 40 • (x + 10)(x + 4) • FOIL to check.

  13. Ex. 12) Factor Completely • x2 – 10x + 16 • (x - 8 )(x - 2) • FOIL to check

  14. Ex. 13) Factor 2x2 –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 x2 + 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) x2 – 2x - 8 • (x + 2 )(x - 4) • Foil to check!!!

  17. Ex. 16) 2x2 + 8x - 42 • 2(x + 7)(x - 3) • FOIL TO CHECK!

  18. Ex 17) Factor: • 3x3 +27x2 + 42x • 3x(x + 2)(x + 7) • FOIL, then distribute 3x to check.

  19. Ex 18) Factor 2x2 + 11x – 21 • Is there a GCF? • NO! • (2x – 3) (x + 7)

  20. Ex 19) Factor 12x2 + x – 20 • Is there a GCF? • No!!!!!!!!! • (4x – 5)(3x + 4) • FOIL to check.

  21. Ex 20) Factor 3x2 +5x - 28 • Is there a GCF? • NO! • (3x – 7) (x + 4) • FOIL to confirm.

  22. Ex. 21) Factor 3x2 – 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: • x² - 36 • 9x² - 64 • x² - 18x + 81 • x² + 7x + 10 • 3x² + 16x + 16 • 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 • (x-15)(x-1) • (x+4)² • (x-24)(x-2) • (x+8)(x-4) • (x+10)(x-3) • (x-12)(x+2) • (x-24)(x+2) • (x+6)(x-4) • (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)

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