College Math Placement Test College Algebra 3

Question 1

What are the zeros of f(x) = x³ - x² - 6x?

Accepted Answer

0, 3, -2

Answer

Factoring gives x(x-3)(x+2) = 0, so the zeros are x = 0, 3, -2.

Question 2

What is the inverse of the function f(x) = (2x + 1) / (x - 3)?

Accepted Answer

f⁻¹(x) = (3x + 1)/(x - 2)

Answer

Swapping x and y gives x(y-3) = 2y+1, then solving for y yields y = (3x+1)/(x-2).

Question 3

A system of equations has 2x + 3y = 12 and 4x - y = 5. What is the value of x?

Accepted Answer

x = 27/14

Answer

Multiplying the second equation by 3 and adding: 14x = 27, so x = 27/14.

Question 4

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

Accepted Answer

x + 2

Answer

x³+8 = (x+2)(x²-2x+4) using the sum of cubes formula a³+b³ = (a+b)(a²-ab+b²).

Question 5

If 3^(2x) = 81, what is x?

Accepted Answer

2

Answer

Since 81 = 3⁴, we have 3^(2x) = 3⁴, so 2x = 4 and x = 2.

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