Questions on Polynomials
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This page contains sample problems on polynomial functions. They
are for Selfassessment and Review. Each
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
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 x^{9} + 7 x^{3} + 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
number?
4. What is the largest number of real roots that a
fourth degree polynomial could have? What is the smallest
number?
5. Describe the large scale, or end behavior of the
following polynomials where a, b, c, d, e, g, are all constants.
 f(x) = x^{6}+ ax^{5} + bx^{4}+
cx^{3}+ dx^{2}+ ex + g
 f(x) = x^{5} + ax^{4}+ bx^{3}+
cx^{2}+ dx + e
6. Find all the zeros or roots of the following
polynomials.
Remember that roots of polynomials may be real or complex.
 g(x) = 3x^{2}  7x  20
 h(x) = x^{2}  4x + 12
 f(x) = 2x^{3} + 6x ^{2}  20x
 f(x) =x^{3}  x^{2}  5x + 5
 p(x) = x^{3} + 3x^{2} + 3x + 2.
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