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.