1. What is the depressed polynomial of (x^3 - 5x^2 + 13x - 14) / (x-2)?

a. x^2 - 2x - +1

b. x^2 -3x +7

c. x^2 -4x +9

d. x^2 -7x +27

2. According to the rational root theorem, which of the following are possible rational roots of 3x^3 + 2x^2 + x -4 = 0 Select all that apply

-2/3

-3/4

1/3

1/4

2. According to the rational root theorem, which of the following are possible rational roots of x^4 +3x^3 + 2x^2 -8x -9 = 0 Select all that apply

-3

-1

1/9

3

3. Which of the following is the upper bound for the zeros of f(x)= 2x^3 -4x^2 - x -2

a. -1

b. 1

c. 2

d. 3

4. Which of the following is an lower bound for the zeros of f(x)= 3x^3 -4x^2 -x +6

a. -2

b. -1

c. 0

d. 1

5. Using descartes rule of sign how many real roots does f(x) = x^4 - x^3 + 2x^2 + x -5 contain

a. no positive real roots, no negative real roots

b. Three or one positive real roots, one or zero negative real roots

c. three or one positive real roots, zero negative real roots

d. Three or one positive real roots, three or one negative real roots