Questions on Polynomials
This page contains sample problems on polynomial functions. They
are for Self-assessment and Review.
problem (or group of problems) has an "answer button" which you
can click to look at an answer. Some solutions have a
"further explanation button"
which you can click to see a more complete, detailed
What to Do To gain
the most benefit from these problems,
problems on your own. Write down your solutions BEFORE
looking at any answers.
Use a graphing calculator as
|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
1. What is the leading term of the polynomial 2 x9 + 7 x3 + 191?
2. Give examples of:
- A polynomial of degree 3
- A polynomial of degree 5 with exactly 3 terms
- A polynomial of degree 4 with exactly 4 terms
3. What is the largest number of real roots
that a 7th degree polynomial could have? What is the smallest
4. What is the largest number of real roots that a
fourth degree polynomial could have? What is the smallest
5. Describe the large scale, or end behavior of the
following polynomials where a, b, c, d, e, g, are all constants.
- f(x) = -x6+ ax5 + bx4+
cx3+ dx2+ ex + g
- f(x) = x5 + ax4+ bx3+
cx2+ dx + e
6. Find all the zeros or roots of the following
Remember that roots of polynomials may be real or complex.
- g(x) = 3x2 - 7x - 20
- h(x) = x2 - 4x + 12
- f(x) = 2x3 + 6x 2 - 20x
- f(x) =x3 - x2 - 5x + 5
- p(x) = x3 + 3x2 + 3x + 2.
7. Are you interested in questions involving