Chapter 5.7: Choosing the Correct Factoring Strategy

With so many different tools used to factor, it is prudent to have a section to determine the best strategy to factor.

Factoring Hints

  1. Look for any factor to simplify the polynomial before you start!
  2. If you have two terms, look for a sum or difference of squares or cubes.

a^2 - b^2 = (a + b)(a - b)a^3 - b^3 = (a - b)(a^2 + ab + b^2)a^3 + b^3 = (a + b)(a^2 - ab + b2)

  1. If you have three terms, see if the master product method works.
  2. If you have four terms, see if factoring by grouping works.

 

Questions

Factor each completely.

  1. 24ac-18ab+60dc-45db
  2. 2x^2-11x+15
  3. 5u^2-9uv+4v^2
  4. 16x^2+48xy+36y^2
  5. -2x^3+128y^3
  6. 20uv-60u^3-5xv+15xu^2
  7. 54u^3-16
  8. 54-128x^3
  9. n^2-n
  10. 5x^2-22x-15
  11. x^2-4xy+3y^2
  12. 45u^2-150uv+125v^2
  13. m^2-4n^2
  14. 12ab-18a+6nb-9n
  15. 36b^2c-16ad-24b^2d+24ac
  16. 3m^3-6m^2n-24n^2m
  17. 128+54x^3
  18. 64m^3+27n^3
  19. n^3+7n^2+10n
  20. 64m^3-n^3
  21. 27x^3-64
  22. 16a^2-9b^2
  23. 5x^2+2x
  24. 2x^2-10x+12

Answers to odd questions

1. 6a(4c-3b)+15d(4c-3b)
(4c-3b)(6a+15d)
3(4c-3b)(2a+5d)

3. -5\times -4=20
-5+-4=-9
5u^2-5uv-4uv+4v^2
5u(u-v)-4v(u-v)
(u-v)(5u-4v)

5. -2(x^3-64y^3)
-2(x-4y)(x^2+4xy+16y^2)

7. 2(27u^3-8)
2(3u-2)(9u^2+6u+4)

9. n(n-1)

11. x^2-3xy-xy+3y^2
x(x-3y)-y(x-3y)
(x-3y)(x-y)

13. (m-2n)(m+2n)

15. 36b^2c-24b^2d+24ac-16ad
12b^2(3c-2d)+8a(3c-2d)
(3c-2d)(12b^2+8a)
4(3c-2d)(3b^2+2a)

17. 2(64+27x^3)
2(4+3x)(16-12x+9x^2)

19. 5\times 2=10
5+2=7
n(n^2+7n+10)
n(n^2+5n+2n+10)
n(n(n+5)+2(n+5))
n(n+5)(n+2)

21. (3x-4)(9x^2+12x+16)

23. x(5x+2)

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