Download 1 Pre-Calc Polynomial Functions Worksheet. 1) Given a polynomial

Pre-Calc Polynomial Functions Worksheet.
1)
Given a polynomial function P ( x) = x 4 − x 3 − 7 x 2 + x + 6
a. List all the factors of the constant term (list the p’s)
b. List all the factors of the leading coefficient (list the q’s)
c. List all the possibilities for rational roots
p

 using the rational zero theorem 
q

d. Use Descartes’ Rule of signs to find the possible number of positive roots
(how many sign changes are there in P(x))
e. Use Descartes’ Rule of signs to find the possible number of negative roots
(how many sign changes are there in P(-x))
f. Test reasonable possibilities to find a single root of P(x) (use either
synthetic division on some easy numbers produced by part c or a table of
values)
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g. Once you find a root synthetically divide to factor out (x-c) where c is
your root.
h. Use part c again and test possible roots in the factored form from part g.
i. Once you find a root use synthetic division to further reduce the
polynomial.
j. Now factor that polynomial
k. What are the 4 roots of P(x)?
l. What is the y-intercept for P(x)?
m. Describe the end behavior of P(x)
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n. Graph P(x) using everything you have found out about it. (DO NOT USE
YOUR CALCULATOR)
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2)
Given a polynomial function P ( x) = 2 x 5 − 13 x 4 − 27 x 3 − 17 x 2 − 5 x + 6
a. List all the factors of the constant term (list the p’s)
b. List all the factors of the leading coefficient (list the q’s)
c. List all the possibilities for rational roots
p

 using the rational zero theorem 
q

d. Use Descartes’ Rule of signs to find the possible number of positive roots
(how many sign changes are there in P(x))
e. Use Descartes’ Rule of signs to find the possible number of negative roots
(how many sign changes are there in P(-x))
f. Test reasonable possibilities to find a single root of P(x) (use either
synthetic division on some easy numbers produced by part c or a table of
values)
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g. Once you find a root synthetically divide to factor out (x-c) where c is
your root.
h. Use part c again and test possible roots in the factored form from part g.
i. Once you find a root use synthetic division to further reduce the
polynomial.
j. Now factor that polynomial
k. What are the roots of P(x)?
l. What is the y-intercept for P(x)?
m. Describe the end behavior of P(x)
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n. Graph P(x) using everything you have found out about it. (DO NOT USE
YOUR CALCULATOR)
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