Algebra 2 by Richard Wright

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4-Review

Take this test as you would take a test in class. When you are finished, check your work against the answers.

    4-01

    Simplify.

  1. (2x2 + 3x − 4) + (−2x2 − 5x + 7)
  2. (5x2 − 4) − (6x2 + 4x + 17)
  3. (2x2 + 3x − 1)(x + 4)
  4. (2x + 1)2

    5. 4-02

    Factor.

  5. x3 + 6x2 + 5x
  6. 4x3 + 2x2 + 16x + 8

    7. Solve by factoring.

  7. 3x3 + 15x2 + 18x = 0
  8. 2x3 + 3x2 − 8x = 12

    9. 4-03

    Divide with long division.

  9. (6x3 + 13x2 + 3x − 2) ÷ (2x2 + 3x − 1)
  10. (9x3 + 6x2 − 23x + 10) ÷ (3x − 2)

    11. Divide with synthetic division.

  11. (3x3 + 7x2 − 14x + 20) ÷ (x + 4)
  12. (2x4 + 3x2 + 5x − 7) ÷ (x − 3)

    13. 4-04

    Use the remainder theorem to evaluate f(x) at the given x value.

  13. 3x3 − 2x2 + x + 18; x = 2
  14. x4 − 5x2 + 3x −20; x = −3

    15. Determine whether the given binomial is a factor of f(x). Show work other than graphing.

  15. f(x) = x3 − x2 − 14x + 24; (x + 4)
  16. f(x) = 6x3 + x2 − 5x − 2; (x − 1)

    17. 4-05

    List the possible rational zeros of the function.

  17. x4 + 2x2 − 4x + 16
  18. 2x3 − 71x2 + 40x − 8

    19. Find all the zeros of the function.

  19. f(x) = 6x3 − 5x2 − 12x − 4
  20. f(x) = x4 − x3 + 2x2 − 4x − 8

Answers

  1. −2x + 3
  2. −x2 − 4x − 21
  3. 2x3 + 11x2 + 11x − 4
  4. 4x2 + 4x + 1
  5. x(x + 1)(x + 5)
  6. 2(2x + 1)(x2 + 4)
  7. −3, −2, 0
  8. −2, −3/2, 2
  9. 3x + 2
  10. 3x2 + 4x − 5
  11. 3x2 − 5x + 6 + \(\frac{-4}{x+4}\)
  12. 2x3 + 6x2 + 21x + 68 + \(\frac{197}{x-3}\)
  13. 36
  14. 7
  15. Yes
  16. No
  17. ±1, ±2, ±4, ±8, ±16
  18. ±1/2, ±1, ±2, ±4, ±8
  19. −2/3, −1/2, 2
  20. −1, 2, ±2i