
Answers to Questions on Polynomial Functions
 Question: What is the degree of the polynomial 2 x^{9} + 7 x^{3} + 191?
Answer: 2 x^{9}
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 There are (infinitely) many right answers to these questions.
 Question: What is an example of a
3rd degree polynomial?
Answer: Any polynomial whose highest degree term is x^{3}. Examples are 5 x^{3} and
x^{3} + 2x^{2}  1
 Question: What is an example of a 5th degree
polynomial with exactly 3 terms?
Answer: An example is
2x^{5}  2x^{2}  10x
 Question: What is an example of a 4th degree
polynomial with exactly 4 terms?
Answer: An example is
x^{4}  x^{3} + 3x + 2
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 Question: What is the largest number
of real roots that a 7th degree polynomial could have? What is the
smallest?
Answer: A seventh degree polynomial has at least
one and at most 7 real roots.
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 Question: How many real roots can a
fourth degree polynomial have?
Answer: 0 to 4, inclusive.
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 Question: What is the large scale
behavior of f(x) = x^{6}+ ax^{5} +
bx^{4}+ cx^{3}+ dx^{2}+ ex + g?
Answer: As x
becomes very large positive or very large negative
f(x) becomes more and more negative.
 Question: What is the large scale behavior of f(x) =
x^{5} + ax^{4}+ bx^{3}+ cx^{2}+ dx + e?
Answer: As x gets large and negative, f(x) becomes
large and negative. As x gets large and positive, f(x) becomes very
large and positive. Return to Exercises
 Question: What are
the roots of g(x) = 3x^{2}  7x  20?
Answer: 5/3 and 4
 Question: What are the roots of h(x) =
x^{2}  4 x + 12?
Answer: complex roots: 2 + 2 sqrt(2) i, and 2  2
sqrt(2) i
 Question: What are the roots of f(x) =
2x^{3} + 6x^{2}  20x?
Answer: 5, 0, and 2
 Question: What are the roots of f(x)
=x^{3}  x^{2}  5x + 5?
Answer: 1, sqrt(5), sqrt(5)
 Question: What are the roots of p(x) =
x^{3} + 3x^{2} + 3x + 2?
Answer: real root: 2, complex roots: 1/2 +
(sqrt(3)/2)i, and 1/2  (sqrt(3)/2)i Return to Exercises
 Question: Are you interested in
questions involving watermelons?
Answer: Here's a hint: How much of the original
load of watermelon was not water?
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