AIME Polynomials and Functions

Question 1

Factor completely: 2x^3 - 8x.

Accepted Answer

2x(x-2)(x+2)

Answer

2x(x^2-4)

Answer

x(2x^2-8)

Answer

2(x^3-4x)

Question 2

If P(x) = x^3 + 2x^2 - 5x - 6 and P(-1) = 0, fully factor P(x).

Accepted Answer

(x+1)(x-2)(x+3)

Answer

(x-1)(x+2)(x-3)

Answer

(x+1)(x+2)(x-3)

Answer

(x-1)(x-2)(x+3)

Question 3

What is the degree of the product of x^3 + 1 and x^2 - x + 1?

Accepted Answer

5

Answer

6

Answer

4

Answer

3

Question 4

Find all rational roots of f(x) = x^3 - 6x^2 + 11x - 6.

Accepted Answer

{1, 2, 3}

Answer

{1, 2, 6}

Answer

{1, 3, 6}

Answer

{2, 3, 6}

Question 5

If f(x) = 2x + 3, find f^(-1)(11).

Accepted Answer

4

Answer

25

Answer

8

Answer

7

Question 6

What is the sum of the roots of 4x^3 - 8x^2 + 5x - 1 = 0?

Accepted Answer

2

Answer

5/4

Answer

1/4

Answer

8