AMC 12 Polynomials & Rational Functions 2

Question 1

If the polynomial x³ + ax² + bx + c has roots 1, 2, and 3, what is a + b + c?

Accepted Answer

-1

Answer

1

Answer

6

Answer

-6

Question 2

Which of the following is a factor of x³ - 8?

Accepted Answer

x² + 2x + 4

Answer

x² - 2x + 4

Answer

x + 2

Answer

x² + 4

Question 3

For the rational function f(x) = (2x² + 3)/(x² - 1), the horizontal asymptote is:

Accepted Answer

y = 2

Answer

y = -3

Answer

y = 0

Answer

y = 3

Question 4

The sum of the squares of the roots of x² - 5x + 3 = 0 equals:

Accepted Answer

19

Answer

25

Answer

13

Answer

22

Question 5

How many vertical asymptotes does f(x) = (x² - 9)/(x² - 4) have?

Accepted Answer

2

Answer

0

Answer

1

Answer

4

Question 6

The polynomial p(x) = x⁴ - 5x² + 4 factors completely over the integers as:

Accepted Answer

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

Answer

(x²-1)(x-4)

Answer

(x-2)²(x+1)²

Answer

(x²+4)(x²-1)

Question 7

For how many distinct real values of x does f(x) = x³ - 4x = 0?

Accepted Answer

3

Answer

1

Answer

2

Answer

4