1. Use the factor theorem to determine if h(x) is a factor of f(x).
h(x) = x – f(x) = x³ + x² -4x + 4

2. Find the quotient and remainder of the following:
5x4 + 5x² x² - x + 1

3. Find the remainder when f(x) is divided by g(x) without using division
f(x) = 10x75 -8x65 + 6x45 + 4x32 -2x15 + 5
g(x) = x - 1

4. For f(x) 2x5 + x4 – 9x² + 4x + 1 find:
Any rational zeros
Use Descartes Rule of signs to find positive and negative zeros
Find an upper and lower bound – show if works or not
List all the real zeros

5. For the following: h(x) .25x4 – 2x³ + 4x² find:
x-intercepts
y-intercepts
Extrema points (how many)
# of points of inflection
Multiplicity
Sketch the graph

6. Find the complete graph of f(x)= x+2
Find domain
Find X-intercepts
Find y-intercepts
Find Vertical Asymptotes
Find any holes
Find Horizontal Asymptotes
Sketch the curve by sign analysis

7. For f(x) x7- 2x6- 5x5+ 13x4- 10x³+ 11x² - 4x - 4 find:
Any rational zeros
Use Descartes Rule of signs to find positive and negative zeros
Find an upper and lower bound – show if works or not
d) List all the real zeros

8. Find the following:
(-i)213

9. Find the following: 3
4+5i

10. Solve the equation and express in factor form:
3x² + 4 = -5x

11. Completely factor f(x) = x4 – 5x³+ 2x²+ 22x - 20