MAT 170 .edu
MAT 170 Name:_____________________________
Quiz 6 Class Time:____________________
Write ANSWERS ONLY in boxes.
1) Given the function p(x) = x2(x – 2)(x + 3)3
a) List all of the zeros d) [pic]
b) What is the degree of p(x)? e) [pic]
c) Which zero has the largest multiplicity? f) Find the Y intercept.
What is its multiplicity?
2) A polynomial, P(x), of degree 6 has zeros of -2, 1, and 4. The zero 1 has a multiplicity of 4. P(3) = 2.
a) Sketch the graph of a polynomial that matches this description
on the plane to the right.
b) [pic]
c) [pic]
3) A polynomial, P(x), of degree 3 has zeros at 2 and -1. 2 has even multiplicity. P(5) = 432.
Find the polynomial P(x). (Leave the answer in factored form) (2 points)
P(x) =
4) (Use the rational zeros theorem to) List all possible rational zeros of the polynomial function
f(x) = 3x7 – 4x6 + 12x4 – 135x3 + x – 12
5) Given the polynomial p(x) = 2x4 – 18x3 + 26x2 + 90x – 100
a) Find all rational zeros.
b) Find all real zeros. (Don’t forget that all rational numbers are also real!)
c) Factor the polynomial p(x)
6) Given the polynomial p(x) = 2x3 – 22x2 + 74x – 70
a) Find all rational zeros.
b) Find all real zeros.
c) Factor the polynomial p(x)
d) [pic]
7) Given g(x) = [pic], Find each of the following. Write “NONE” if there is no answer.
Vertical Slant
Asymptotes Asymptote
Horizontal Holes at
Asymptote x =
Y intercept X intercepts
8) Given g(x) = [pic], Find each of the following. Write “NONE” if there is no answer.
Vertical Slant
Asymptotes Asymptote
Horizontal Holes at
Asymptote x =
Y intercept X intercepts
9) Write an equation of a rational function, f(x), with vertical asymptotes at x = 3 and x = 0, horizontal asymptote at y = 0, a single X intercept when x = 4, a hole in the graph when x = 2, and f(x) = 9 when x = 1.
(Leave the answer in factored form.)
f(x) =
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[pic]
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