ALGEBRA

ALGEBRA
1. Find all real solutions. Your answer should be in exact form, not a decimal approximation.
(x2 – 1) 2 – (x 2 – 1) – 2 = 0
2. Find all complex solutions: x 2 – 4x + 7 = 0
3. The profit for making and selling x gizmos is P(x) = – x 2 + 20x + 100. How many gizmos should be sold to maximize the profit? What is the maximum profit?

4. Solve the inequality x 2 – 7x < – 10 . Write your answer using interval notation.

5. Find the degree, the leading term, the leading coefficient, the constant term, and the end behavior of the polynomial
P(x) = – x 4 + 5x 3 + 7x – 2

6. Find the zeroes of the polynomial function f(x) = (x + 4) 3(x – 1), and state the multiplicity of each. Does the graph cross or touch the x-axis at the zero?
7. Using the Intermediate Value Theorem, determine whether the function has at least one real zero between a and b.
f(x) = x 3 + 3x 2 – 9x – 13 a = -5 b = -4

8. For the function g(x) = x^3/(2x^3-x^2-3x)determine

a. the vertical asymptotes, if any
b. the holes, if any
c. the horizontal asymptotes, if any
d. the oblique asymptote, if any

9. Find all solutions. Be sure to check for extraneous solutions:

5/(x+2)- 4/(x^2-4) = (x-3)/(x-2)
10. Solve the rational inequality (x-2)/(x+3)> 0. Express your answer using interval notation.

11. 5 – 3√t2 + 1 = 1