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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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