Questions on Polynomials


What's On This Page

This page contains sample problems on polynomial functions. They are for Self-assessment and Review.

Each problem (or group of problems) has an "answer button" ANSWER which you can click to look at an answer. Some solutions have a "further explanation button" Explain which you can click to see a more complete, detailed solution.

What to Do

To gain the most benefit from these problems,

Work the problems on your own. Write down your solutions BEFORE looking at any answers.

Use a graphing calculator as appropriate.

If you have difficulties with this material, please contact your instructor. (See Getting Help in Stage 1.) It will be very difficult to succeed in Calculus without understanding polynomial functions.


1. What is the leading term of the polynomial 2 x9 + 7 x3 + 191?

ANSWER

2. Give examples of:

  1. A polynomial of degree 3

  2. A polynomial of degree 5 with exactly 3 terms

  3. A polynomial of degree 4 with exactly 4 terms

ANSWER

3. What is the largest number of real roots that a 7th degree polynomial could have? What is the smallest number?

ANSWER

4. What is the largest number of real roots that a fourth degree polynomial could have? What is the smallest number?

ANSWER

5. Describe the large scale, or end behavior of the following polynomials where a, b, c, d, e, g, are all constants.

  1. f(x) = -x6+ ax5 + bx4+ cx3+ dx2+ ex + g

  2. f(x) = x5 + ax4+ bx3+ cx2+ dx + e

ANSWER

6. Find all the zeros or roots of the following polynomials. Remember that roots of polynomials may be real or complex.

  1. g(x) = 3x2 - 7x - 20

  2. h(x) = x2 - 4x + 12

  3. f(x) = 2x3 + 6x 2 - 20x

  4. f(x) =x3 - x2 - 5x + 5

  5. p(x) = x3 + 3x2 + 3x + 2.

ANSWER

7. Are you interested in questions involving watermelons?

ANSWER

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