Factoring Review

EQ: How do I factor polynomials?

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!

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!

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)

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

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!!!!!!!!!!!!

Ex. 6-7: Practice

Factor Completely!Ex. 6) X2 – 4Ex. 7) 36a2 – 49b2

6. (x + 2)(x – 2)7. (6a + 7b)(6a – 7b)

Perfect Square Trinomial

• x²+bx+c• What multiplies to give you “c” and adds

to give you “b”?• Your answer is a binomial squared

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

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.

Lets change the sign of the middle term Example 10:

• x2 – 6x + 8

• (x – 2)(x – 4)• Check by FOIL.

Ex. 11) Factor Completely

• x2 + 14x + 40

• (x + 10)(x + 4)• FOIL to check.

Ex. 12) Factor Completely

• x2 – 10x + 16

• (x - 8 )(x - 2) • FOIL to check

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!

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!

Ex. 15) x2 – 2x - 8

• (x + 2 )(x - 4)• Foil to check!!!

Ex. 16) 2x2 + 8x - 42

• 2(x + 7)(x - 3) • FOIL TO CHECK!

Ex 17) Factor:

• 3x3 +27x2 + 42x

• 3x(x + 2)(x + 7)

• FOIL, then distribute 3x to check.

Ex 18) Factor 2x2 + 11x – 21

• Is there a GCF?• NO!• (2x – 3) (x + 7)

Ex 19) Factor 12x2 + x – 20

• Is there a GCF?• No!!!!!!!!! • (4x – 5)(3x + 4)• FOIL to check.

Ex 20) Factor 3x2 +5x - 28

• Is there a GCF?• NO!• (3x – 7) (x + 4)• FOIL to confirm.

Ex. 21) Factor 3x2 – x - 6

• Prime!!!!

Homework

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

Do Now:

• Factor the following:1. x² - 362. 9x² - 643. x² - 18x + 814. x² + 7x + 105. 3x² + 16x + 166. 4x² - 32x + 64

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)²30. 3(x+2)31. 3(x²+6)

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)

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)

Pg. 296, 40-57

40. (x-15)(x-1)41. (x+4)²42. (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)