$$x \leq 0 or$$ $$x \u003e 2$$,\ x \neq 2$

Question 1

Which of the following is the correct solution set for the inequality $$x^2 - 3x$$ \u003e 4$$?

Accepted Answer

$$x  4$$

Question 2

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

Accepted Answer

$$x \leq 0 or$$ $$x \u003e 2$$,\ 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

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