Honors Algebra 2: Factoring Extra Practice

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Factor Completely:

  1. \( 40zw + 8x^{2}w - 35z - 7x^{2}\)
    2. Solution \( \left(5z + x^{2}\right)\left(8w - 7\right) \)
  2. \( a^{3} - a^{2}b + ab^{2} - b^{3}\)
    3. Solution \( \left(a^{2} + b^{2}\right)\left(a - b\right) \)
  3. \( a^{6} - b^{6}\)
    4. Solution \( \left(a - b\right)\left(a^{2} + ab + b^{2}\right)\left(a + b\right)\left(a^{2} - ab + b^{2}\right) \)
  4. \( x^{4} + 25\)
    5. Solution Non-factorable
  5. \( 6x^{2} + 42x + 60\)
    6. Solution \( 6\left(x + 2\right)\left(x + 5\right) \)
  6. \( 4x^{2}- 24x + 36\)
    7. Solution \( 4\left(x - 3\right)^{2} \)
  7. \( 75x^{2} + 120x + 48\)
    8. Solution \( 3\left(5x + 4\right)^{2} \)
  8. \( 36 - 9x^{2}\)
    9. Solution \( -9\left(x + 2\right)\left(x - 2\right) \)
  9. \( 2x^{2}y + xy - 2xz - z\)
    10. Solution \( \left(2x + 1\right)\left(xy - z\right) \)
  10. \( 12x^{2}z + 8y^{2}z - 15x^{2}w - 10y^{2}w\)
    11. Solution \( \left(3x^{2} + 2y^{2}\right)\left(4z - 5w\right) \)
  11. \( y^{6} + 7y^{3} - 8\)
    12. Solution \( \left(y + 2\right)\left(y^{2} - 2y + 4\right)\left(y - 1\right)\left(y^{2} + y + 1\right) \)
  12. \( (x + y)^{3} - 27\)
    13. Solution \( \left(x + y - 3\right)\left(x^{2} + 2xy + y^{2} +3x + 3y + 9\right) \)
  13. \( x^{2} + 2x + 5\)
    14. Solution Non-factorable
  14. \( x^{16} - 1\)
    15. Solution \( \left(x^{8} + 1\right)\left(x^{4} + 1\right)\left(x^{2} + 1\right)\left(x + 1\right)\left(x - 1\right) \)
  15. \( 5x^{2} - 42x - 27\)
    16. Solution \( \left(5x + 3\right)\left(x - 9\right) \)
  16. \( 6a^{2} - 13a - 15\)
    17. Solution \( \left(6a + 5\right)\left(a - 3\right) \)
  17. \( 15y^{2} + 17y - 18\)
    18. Solution \( \left(5a + 9\right)\left(3y - 2\right) \)
  18. \( 14 p^{2} + 31p - 10\)
    19. Solution \( \left(7p - 2\right)\left(2p + 5\right) \)
  19. \( 16t^{4} - 81\)
    20. Solution \( \left(2t - 3\right)\left(2t + 3\right)\left(4t^{2} + 9\right) \)
  20. \( 81m^{8}- 1\)
    21. Solution \( \left(3m^{2} - 1\right)\left(3m^{2} + 1\right)\left(9m^{4} + 1\right) \)
  21. \( 3z^{6} - 192\)
    22. Solution \(3\left(z - 2\right)\left(z^{2} + 2z + 4\right)\left(z + 2\right)\left(z^{2} - 2z + 4\right) \)
  22. \( 6u^{6} - 8v^{3}\)
    23. Solution \( 2\left(3a^{6} - 4v^{3}\right) \)
  23. \( 16y^{4} - 72y^{2} + 81\)
    24. Solution \( \left(2y - 3\right)^{2}\left(2y + 3\right)^{2} \)
  24. \( (x - 1)^{2} - y^{2}\)
    25. Solution \( \left(x - 1 + y\right)\left(x - 1 - y\right) \)
  25. \( (r + s)^{2} - t^{2}\)
    26. Solution \( \left(r + s + t\right)\left(r + s - t\right) \)
  26. \( 3ax - 6bx - 4a + 8b\)
    27. Solution \( \left(3x - 4\right)\left(a - 2b\right) \)
  27. \( (x + y)^{2} + 3(x + y) + 2\)
    28. Solution \( \left(x + y + 1\right)\left(x + y + 2\right) \)
  28. \( x^{4} - 3x^{2} - 40\)
    29. Solution \( \left(x^{2} - 8\right)\left(x^{2} + 5\right) \)
  29. \( x^{2a} - 3x^{a} + 2 \quad \forall a \in \mathbb{Z}\)
    30. Solution \( \left(x^{a} - 1\right)\left(x^{a} - 2\right) \)
  30. \( r^{2k} + 6r^{k} + 9 \quad \forall k \in \mathbb{Z}\)
    31. Solution \( \left(r^{k} + 3\right)^{2} \)
  31. \( h^{3} + 4h^{2} - 9h - 36\)
    32. Solution \( \left(h + 3\right)\left(h - 3\right)\left(h + 4\right) \)
  32. \( x^{2} - y^{2} + 4y - 4x\)
    33. Solution \( \left(x + y - 4\right)\left(x - y\right) \)
  33. \( x^{4} - (4x - 5)^{2}\)
    34. Solution \( \left(x^{2} - 4x + 5\right)\left(x - 1\right)\left(x + 5\right) \)
  34. \( (a + 5)^{2} + 12(a + 5) + 36\)
    35. Solution \( \left(a + 11\right)^{2} \)
  35. \( 2a^{4} + 10a^{3} - 72a^{2}\)
    36. Solution \( 2a^{2}\left(a + 9\right)\left(a - 4\right) \)
  36. \( 9x^{2}y^{3} + 72x^{5}\)
    37. Solution \( 9x^{2}\left(y + 2x\right)\left(y^{2}- 2xy + 4x^{2}\right) \)

In the problem sets on §4.5 (p. 185) and §4.6 (p. 191) I only assigned even problems. Do the odd problems for extra practice. The answers are in the back of the book.