 # Math 150 Week in Review 5 Problem Set

1. Determine the end behavior of the following polynomials .

(a) P(x) = 5x8 + 6x7−4x−9

(b) P(x) = −10x11 − 5x6 + 5x2 − 2

2. Sketch graphs for the following polynomials.

(a) P(x) = 2x3 − x2 − 10x (b) P(x) = (x − 1)2(x + 1)3(3 − x) 3. Use long division to nd the quotient and remainder of the following.
(a) (b) 4. Find the polynomial of degree 4 with zeros 1,−2,and 3, where 1 is a zero of multiplicity 2 and the
constant
term is 18.

5. Evaluate the following expressions and write in standard form.

(a) i30

(b) (c) 6. Solve the equation 3x2−2x =−1.

7. Find all intercepts , vertical or horizontal asymptotes, and holes for the following rational functions .

(a) (b) 8. Sketch graphs for the following rational functions .

(a)  (b)  Your instructor may or may not have covered the following:

9. Which of the rational functions in Problems 7 and 8 has a slant (oblique) asymptote? What is its
slant (oblique) asymptote?

10. Use synthetic division to find the quotient and remainder when x3−8x−5 is divided by x + 3.

11. Factor the polynomial P(x) = 2x3−3x2−17x + 30 completely if it is known that 5/2 is a zero of the polynomial.

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