Question 1

Which of the following is the correct domain of the function $$f(x) = \frac{x^2$-9}{x^2$+5}$$?

Accepted Answer

$$x \in \mathbb{R}$$

Question 2

Simplify the expression $$\$$left(2x^3$$y^{-2}z^4$y^{-5}z^2$\$$right)^2$$ and choose the correct answer.

Accepted Answer

$$4x^6y$$^{-14}$$z^{10}$$

Question 3

Which of the following is the correct factorization of $$x^2 + 22x + 121$?

Accepted Answer

$$(x + 11)(x + 11)$$

Question 4

Given the rational expression $$\frac{2x^2$y+5xy-3y}{y^2$-2xy^3$$}$, which of the following is a restriction on the domain?

Accepted Answer

$$y 
eq 0$$

Question 5

If $$a^0 = 1$ for any nonzero a$, what is the value of (-3)^0$ + 2^0$?

Accepted Answer

$$2$$

Question 6

Which of the following is the correct simplification of $$\sqrt[3]{81m^9$p^{15}$$}$?

Accepted Answer

$$9m^3p^5$

Question 7

A chemical solution is modeled by the polynomial $$8x^4$$ - $$3x^2 - 1$. What is the degree and leading coefficient of this polynomial?

Accepted Answer

Degree: 4, Leading coefficient: 8

Question 8

Which of the following is the correct result of $$\left(3x - 7\$$right)^2$$?

Accepted Answer

$$9x^2 - 42x + 49$

Question 9

A medical researcher is analyzing the function $$f(x) = \sqrt{x-4}. $$What is the domain of $$f(x)$$?

Accepted Answer

$$x \geq 4$$

Question 10

Simplify the expression $$\left(\frac{a^2$}{b^3$}\$$right)^{-2/3}$$.

Accepted Answer

$$\frac{b^2$}{a^4$}$$

Question 11

Which of the following is the correct simplification of $$\frac{3}{\sqrt{7}}$$ after rationalizing the denominator?

Accepted Answer

$$\frac{3\sqrt{7}}{7}$$

Question 12

A biologist is modeling population growth with the function $$P(t) = 5t^2$ - 2t + 8. $$What is the value of $$P(3)$$?

Accepted Answer

$$43$$

Question 13

Which of the following is the correct result of $$\frac{8}{x+4} - \frac{3}{x-6}$$, simplified and left in factored form?

Accepted Answer

$$\frac{8(x-6) - 3(x+4)}{(x+4)(x-6)}$$

Question 14

Which of the following is the correct simplification of $$\frac{x^2$-6x-5}{x^2$+4x-5} \div \frac{x^2$+4x-5}{x^2$-8x+15}$$?

Accepted Answer

$$\frac{x^2$-6x-5}{x^2$-8x+15}$$

Question 15

Which of the following is the correct result of $$\sqrt{64x^3$y^5z^4$}$$, assuming all variables are positive?

Accepted Answer

$$8x^{1}y$$^{2}$$z^{2}$$\sqrt{xy}$$

Question 16

A pharmaceutical company needs to factor $$x^2 - 4x + 4$. Which of the following is the correct factorization?

Accepted Answer

$$(x-2)^2$$

Question 17

Which of the following is the correct simplification of $$\frac{2x^2$y+5xy-3y}{y^2$-2xy^3$$}$?

Accepted Answer

$$\frac{2x^2$y+5xy-3y}{y^2$-2xy^3$$}$

Question 18

Which of the following is the correct simplification of $$\left(\frac{x^2$y^3$$}{$$y^2x^5$}\$$right)^{-2}$$?

Accepted Answer

$$\frac{x^6$}{y^2$}$$

Question 19

A physicist is working with the function $$f(x) = \frac{1}{x^2$-9}. $$Which of the following values is NOT in the domain of $$f(x)$$?

Accepted Answer

$$x = 3$$

College Algebra: Essential Concepts and Skills Study Guide

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