Download Alg 2B

Alg 2B
Test Review Polynomials and Rational Functions
Factor the polynomial to find the zeros and write the factored form.
Describe the end behavior of the function. Without a calculator, sketch the
graph.
1.) P(x) = 3x3-6x
3.) P(x) = x5-9x3 + 20x2
Graph the polynomial and determine how many local maxima and minima it
has.
4.) y = 2x4-36
5.) y = x3-9x
Find the quotient and remainder using long division.
6.) 6x3+2x2+22x+9
2x+5
Find all the real zeros and the factored form of the polynomial. Use the
quadratic formula if necessary.
10.) P(x) = 2x3+x2-13X+6
11.) P(X) = X4-5X3-5X2+ 23X + 10
13. Give examples of polynomials with the following properties or explain why
it is impossible to have a polynomial with the properties:
a) a polynomial of degree 3 with no real zeros
b) a polynomial of degree 4 with no real zeros
c) a polynomial of degree 3 with 3 real zeros, only 1 of which is
rational
d) a polynomial of degree 4 that has 4 real zeros, none of which is
rational
14. Given the graph of f(x), write a possible factorization for the
equation of the function.
15. Using proper notation, describe the end behavior for f(x) = -3x5+ 5x + 2
16. Write a polynomial function with degree 5 that has three real zeros
at x = 4, x = -2, and x = √3.
Analyze the following rational functions. Find domain, x and y intercepts,
find equations of asymptotes and describe with limit notation
16. y = (3x-2)/(5x-10)
17. Y = (x-2)/(x2 – 4)
18. y = 4/(x2 + 1)
19. Y = 3x/(x2 + x)
20. What is a discontinuity in a function? Name the two types of
discontinuities and how you can determine them algebraically and identify
them graphically.
Simplify the following expressions.
21. [3x5/(x2 – 2x) ]* [(x2 – 4)/9x]
22. (2x2 + 5x + 2)/(2x2 – 18) divided by (x2 + 7x + 10)/(5x + 15)
23. 2/(x+4)2 - 5/(x2 – 16)
24. 3/5x + 4x/15x2
Solve
25. 3/(x-5) + 2 = 4/(x+2)