1. Find a fifth degree polynomial that will have the zeros 0, 1, -2 and i.
a.x5 + x4 - x3 + x2 - 2x
b.x5 - x4 - x3 + x2 - 2x
c.x4 + x3 - 2x2 - ix3 - ix2 +2ix
d.x4 - x3 - 2x2 - ix3 + ix2 +2ix
e.none of these
2. Find a fourth degree polynomial that has zeros 1 (with a multiplicity of 2) and 1 i.
a.x2 2x ix + 1 i
b.x2 + 2x ix + 1 i
c.x4 4x3 + 7x2 4x + 2
d.x4 + 2x3 + x2 + 2ix2 + 4ix + 2i
e.none of these
Questions 3 12 refer to the polynomial
f(x) = x5 + x4 - 15x3 - x2 + 38x - 24.
3. How many positive real zeros MIGHT this polynomial have?
a.4 or 2 or 0
b.3 or 1
c.4 or 2
d.3 or 1 or 0
e.none of these
4. How many negative real zeros MIGHT this polynomial have?
a.4 or 2 or 0
b.3 or 1
c.4 or 2
d.3 or 1 or 0
e.none of these
5. What are the POSSIBLE rational zeros?
a.+- 2, +- 3, +- 4, +- 6, +- 8, +- 12
b.1, 2, 3, 4, 6, 8, 12, 24
c.+- 1, +- 2, +- 3, +- 4, +- 6, +- 8, +- 12, +- 24
d.+- 1, +- 24
e.none of these
6. Use synthetic division to identify all rational zeros.
a.1, 2, 3, 4
b.4, -2, 1, 3
c.4, -3, -2, -1
d.3, -1, 2, 4
e.none of these
7. Are there any complex zeros? If so, what are they?
a.yes, i and i
b.yes, 2i and 2i
c.yes, i and 2i
d.yes, -i and 2i
e.none of these
8. Factor the polynomial completely.
a.(x 1)(x 2)(x 3)(x 4)
b.(x + 1)(x + 2)(x + 3)(x + 4)
c.(x+1)2(x 2)(x + 3)(x 4)
d.(x 1)2(x + 2)(x 3)(x + 4)
e.none of these
9. What are the x-intercepts of the graph of this polynomial?
a.1, 2, 3, 4
b.4, -2, 1, 3
c.4, -3, -2, -1
d.3, -1, 2, 4
e.none of these
10. What is the multiplicity of the smallest zero, and what does this say about the graph?
i.multiplicity is 1
ii.multiplicity is 2
iii.multiplicity is 3
iv.graph touches the x-axis at this intercept
v.graph goes through the x-axis at this intercept.
a.i and iv
b.i and v
c.ii and iv
d.ii and v
e.iii and iv
f.iii and v
g.none of these
11. What is the y-intercept of this function (where does the graph cross the y-axis)?
a.1
b.0
c.24
d.24
e.none of these
12. What is the end-behavior of the graph (does it rise or fall at each end)?
a.rises at both ends
b.falls at both ends
c.rises at left end, falls at right end
d.falls at left end, rises at right end
e.none of these
13. The answer to this question is E. 
Questions 14 23 refer to the polynomial
f(x) = x4 4x3 + 7x2 16x + 12.
14. How many positive real zeros MIGHT this polynomial have?
a.4 or 2 or 0
b.3 or 1
c.4 or 2
d.3 or 1 or 0
e.none of these
15. How many negative real zeros MIGHT this polynomial have?
a.4 or 2 or 0
b.3 or 1
c.4 or 2
d.3 or 1 or 0
e.none of these
16. What are the POSSIBLE rational zeros?
a. 2,  3,  4,  6
b.1, 2, 3, 4, 6, 12
c. 1,  2,  3,  4  6,  12
d. 1,  12
e.none of these
17. Use synthetic division to identify all rational zeros.
a.1, 3
b.-1, -3
c.1, -3
d.1, 3
e.none of these
18. Are there any complex zeros? If so, what are they?
a. yes, i and i
b.yes, 2i and 2i
c.yes, i and 2i
d.yes, -i and 2i
e.none of these
19. Factor the polynomial completely.
a.(x 1)(x 3)(x 2i)(x + 2i)
b.(x + 1)(x + 3)(x 2i)(x + 2i)
c.(x 1)(x 3)(x i)(x + i)
d.(x + 1)(x + 3)(x i)(x + i)
e.none of these
20. What are the x-intercepts of the graph of this polynomial?
a.1, 3
b.-1, -3
c.1, -3
d.1, 3
e.none of these
21. What is the multiplicity of the smallest zero, and what does this say about the graph?
i.multiplicity is 1
ii. multiplicity is 2
iii. multiplicity is 3
iv. graph touches the x-axis at this intercept
v. graph goes through the x-axis at this intercept.
a.i and iv
b.i and v
c.ii and iv
d.ii and v
e.iii and iv
f.iii and v
g.none of these
22. What is the y-intercept of this function (where does the graph cross the y-axis)?
a.0
b.1
c.12
d.12
e.none of these
23. What is the end-behavior of the graph (does it rise or fall at each end)?
a.rises at both ends
b.falls at both ends
c.rises at left end, falls at right end
d.falls at left end, rises at right end
e.none of these
24. Solve the system
{2x-3y=4
{x+y=-3
If the solution point is (x , y), what is the product xy? (ie, multiply the coordinates of the solution point)
a.0
b.2
c.1
d.12
e.none of these
25. Solve the system
{2x-3y=4
{4x-6y=-3
If the solution point is (x , y), what is the product xy? (ie, multiply the coordinates of the solution point)
a.0
b.2
c.1
d.12
e.none of these