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 $\left(2x^3y^{-2}z^4y^{-5}z^2\right)^2$ 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 $\frac{2x^2y+5xy-3y}{y^2-2xy^3}$, 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 $\sqrt[3]{81m^9p^{15}}$?

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 $\sqrt{64x^3y^5z^4}$, 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 $\frac{2x^2y+5xy-3y}{y^2-2xy^3}$?

Accepted Answer

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

Question 18

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

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

Study Guide - Practice Questions