$x \leq 0$ or $x > 2$,\ x \neq 2$

Question 1

Which of the following is the correct solution set for the inequality $x^2 - 3x > 4$?

Accepted Answer

$x < -1$ or $x > 4$

Question 2

Given the rational inequality $\frac{x^2}{x-2} \geq 0$, which of the following describes the solution set?

Accepted Answer

$x \leq 0$ or $x > 2$,\ x 
eq 2$

Question 3

Solve for $x$ in the equation $x^2 + 4x = 5$.

Accepted Answer

$x = -2 \pm \sqrt{9}$

Question 4

Given $f(x) = x^4 - 16x^2 + 36$, how many real and complex solutions does the equation $f(x) = 0$ have?

Accepted Answer

4 real, 0 complex

Question 5

Which of the following is a factor of $x^4 - 5x^2 + 4x - 20$?

Accepted Answer

$x^2 + 4$

Question 6

Find all solutions to $x^3 - 2x^2 + 9x + 18 = 0$.

Accepted Answer

$x = -3, x = 2 \pm i\sqrt{5}$

Question 7

Construct a third degree polynomial with roots $x = 2$, $x = 0$, and $x = -1$.

Accepted Answer

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

Question 8

Find all solutions to $x^4 - 5x^2 + 4x - 20 = 0$.

Accepted Answer

Cannot be factored with integer roots; requires quadratic formula

Question 9

Given $f(x) = 2x^3 - 5x^2 + 10x$, use synthetic division to find $f(1)$.

Accepted Answer

$7$

Question 10

Simplify $\sqrt{27} - \sqrt{12}$.

Accepted Answer

$3\sqrt{3} - 2\sqrt{3} = \sqrt{3}$

Question 11

Which of the following is the correct simplification for $\sqrt{75} + \sqrt{12}$?

Accepted Answer

$5\sqrt{3} + 2\sqrt{3} = 7\sqrt{3}$

Question 12

If $x^2 - 3x + 2 = 0$, what are the solutions for $x$?

Accepted Answer

$x = 1, x = 2$

Question 13

Which of the following is the correct factorization of $x^3 + 3x^2 - 4x$?

Accepted Answer

$x(x^2 + 3x - 4)$

Question 14

Which of the following is a possible rational root of $x^3 - 2x^2 + 9x + 18$ according to the Rational Root Theorem?

Accepted Answer

$x = -3$

Question 15

If $x^2 + 4x + 4 = 0$, what is the solution for $x$?

Accepted Answer

$x = -2$

Question 16

Which of the following is the correct simplification for $\sqrt{81} - 7$?

Accepted Answer

$2$

Question 17

If $x^2 - 4x + 4 = 0$, what is the multiplicity of the root?

Accepted Answer

2

Question 18

Which of the following is the correct solution for $x^2 + 2x + 2 = 0$?

Accepted Answer

$x = -1 \pm i$

Question 19

If $x^3 - 8 = 0$, what is the real solution for $x$?

Accepted Answer

$x = 2$

Question 20

Which of the following is the correct factorization of $x^4 - 16$?

Accepted Answer

$(x^2 - 4)(x^2 + 4)$

Precalculus Test Review: Equations, Inequalities, and Polynomial Functions

Study Guide - Practice Questions