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Polynomial Functions Practice Test

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By — McGraw-Hill Professional
Updated on Oct 4, 2011

Review the following concepts if needed:

Polynomial Functions Practice Test

Problems

  1. What are the x -intercepts of f(x) = x 2 ( x + 3)( x − 2)?

    (a) −3 and 2 (b) 3 and −2 (c) 0, −3, and 2 (d) 0, 3, and −2

     

    Polynomial Functions Chapter 7 Review

    Fig. 7.20

  2. The graph in Figure 7.20 is the graph of which function?

    (a) f(x) = 2 x 2 ( x − 1)( x + 2) = 2 x 4 + 2 x 3 − 4 x 2

    (b) f(x) = −2 x 2 ( x − 1)( x + 2) = −2 x 4 − 2 x 3 + 4 x 2

    (c) f(x) = 2 x ( x − 1)( x + 2) = 2 x 3 + 2 x 2 − 4 x

    (d) f(x) = −2 x ( x − 1)( x + 2) = −2 x 3 − 2 x 2 + 4 x

  3. What is the quotient and remainder for

    Polynomial Functions Chapter 7 Review

    (a) The quotient is x − 1, and the remainder is − 3 x 3.

    (b) The quotient is x − 1, and the remainder is − x + 3.

    (c) The quotient is x + 1, and the remainder is x + 3.

    (d) The quotient is x + 1, and the remainder is 3 x + 3.

  4. Use synthetic division to find the quotient and remainder for (2 x 3x 2 + 2 x + 4) ÷ ( x − 3).

    (a) The quotient is 2 x 2 + x + 5, and the remainder is 19.

    (b) The quotient is 2 x 2 + 5 x + 7, and the remainder is 29.

    (c) The quotient is 2 x 2 + 5 x + 17, and the remainder is 55.

    (d) The quotient is 2 x 2 + x + 3, and the remainder is 7.

  5. What is the quotient for ( x 4 + x 3 − 3 x + 5) ÷ (−2 x 2 + x − 6)?

    Polynomial Functions Chapter 7 Review

  6. Completely factor P ( x ) = 4 x 3 + 4 x 2x − 1.

    (a) ( x − 1) 2 (4 x + 1)

    (b) ( x + 1)(2 x − 1)(2 x + 1)

    (c) ( x + 1) 2 (4 x − 1)

    (d) ( x − 1)(2 x − 1)(2 x + 1)

  7. Find all solutions for x 2 + 2 x + 4 = 0.

    Polynomial Functions Chapter 7 Review

  8. What is the quotient for Polynomial Functions Chapter 7 Review ?

    Polynomial Functions Chapter 7 Review

  9. According to the Rational Zero Theorem, which is NOT a possible rational zero for f(x) = 4 x 5 − 6 x 3 + 2x 2 − 6 x − 9?

    (a) −4 Polynomial Functions Chapter 7 Review (c) 3 (d) −9

  10. According to Descartes’ Rule of Signs, how many positive zeros does f(x) = 4 x 5 − 6 x 3 + 2 x 2 − 9 have?

    (a) 3 (b) 2 or 0 (c) 2 (d) 3 or 1

  11. Find all zeros for f(x) = x 3 − 6 x 2 + 13 x − 10.

    (a) −2, 2 ± i (b) 2, 2 ± i (c) 2, 1 ±2 i (d) −2, 1 ±2 i

Solutions

  1. C
  2. A
  3. B
  4. C
  5. D
  6. B
  7. A
  8. D
  9. A
  10. D
  11. B
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