San Diego State University Polynomial with Integer Coefficients Questions

College Algebra—Exam 3Show all your work for full credit, total 100 points
Name: _________________________
Q1. (10 points) For the polynomial function 𝑔(𝑥) = 3𝑥 7 − 𝑥 5 + 5𝑥 4 + 𝑥 3 + 8
a) List the potential rational zeros.
b) Use Descartes Rule of Signs to determine how many positive and negative real zeros
each polynomial function may have. Do not attempt to find the zeros.
Q2. (10 points) Find a polynomial with integer coefficients that satisfies the given condition.
Q has degree 3 and zeros −3 and 1 + 𝑖
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College Algebra—Exam 3
Show all your work for full credit, total 100 points
Name: _________________________
Q3. (20 points) Given 𝑃(𝑥) = 𝑥 4 − 2𝑥 3 − 2𝑥 2 − 2𝑥 − 3
a) Use synthetic division to find the quotient and remainder when 𝑃(𝑥) is divided by 𝑥 − 1
b) Is (𝑥 − 3) a factor of 𝑃(𝑥)?
c) Find all the real and complex zeros for 𝑃(𝑥)
d) Graph 𝑃(𝑥)
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College Algebra—Exam 3
Show all your work for full credit, total 100 points
Name: _________________________
Q4. (10 points) Find the intercepts and asymptotes, and then sketch a graph of the rational
function and state the domain and range.
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𝑟(𝑥 ) =
𝑥−2
3
College Algebra—Exam 3
Show all your work for full credit, total 100 points
Name: _________________________
Q5. (10 points)
Solve the inequality 2𝑥 2 > 𝑥 + 3
𝑥+2
Q6. (10 points) Solve the inequality
𝑥 2 −9
4
≤0
College Algebra—Exam 3
Show all your work for full credit, total 100 points
Name: _________________________
Q7. (10 points) Find the common factors of the numerator and denominator of the rational
function. Then find the intercepts and asymptotes and sketch a graph. State the domain and
range.
𝑟(𝑥) =
𝑥 2 − 2𝑥 − 3
𝑥−3
5
College Algebra—Exam 3
Show all your work for full credit, total 100 points
Name: _________________________
Q8. (20 points) Given 𝑟(𝑥)
find its domain, label all intercepts, vertical asymptotes, horizontal asymptotes, and oblique
asymptotes. Then graph it
𝑥2 + 𝑥 − 2
(𝑥 − 1)(𝑥 + 2)
𝑟(𝑥) = 2
=
𝑥 − 2𝑥 − 3 (𝑥 + 1)(𝑥 − 3)
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