# math_150_week_in_review_5_problem_set-mswaosfbwf

# Math 150 Week in Review 5 Problem Set

1. Determine the end behavior of the following polynomials .

(a) P(x) = 5x^{8} + 6x^{7}−4x−9

(b) P(x) = −10x^{11}
− 5x^{6} + 5x^{2} −
2

2. Sketch graphs for the following polynomials.

(a) P(x) = 2x^{3} − x^{2}
− 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) i^{30}

(b)

(c)

6. Solve the equation 3x^{2}−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 x^{3}−8x−5
is divided by x + 3.

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

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