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Chapter 7: Factoring

7.7 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.
    • a2b2=(a+b)(ab)a3b3=(ab)(a2+ab+b2)a3+b3=(a+b)(a2ab+b2)
  3. If you have three terms, see if the master product method works.
  4. If you have four terms, see if factoring by grouping works.

If you find that you have trouble factoring the questions in this section, then you might need to redo from the start of Chapter 7. This is not uncommon.

Questions

Factor each completely.

  1. 24ac18ab+60dc45db
  2. 2x211x+15
  3. 5u29uv+4v2
  4. 16x2+48xy+36y2
  5. 2x3+128y3
  6. 20uv60u35xv+15xu2
  7. 54u316
  8. 54128x3
  9. n2n
  10. 5x222x15
  11. x24xy+3y2
  12. 45u2150uv+125v2
  13. m24n2
  14. 12ab18a+6nb9n
  15. 36b2c16ad24b2d+24ac
  16. 3m36m2n24n2m
  17. 128+54x3
  18. 64m3+27n3
  19. n3+7n2+10n
  20. 64m3n3
  21. 27x364
  22. 16a29b2
  23. 5x2+2x
  24. 2x210x+12

Answer Key 7.7

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