Question 1

Which of the following is the correct prime factorization of $126$?

Accepted Answer

$2 	imes 3^2 	imes 7$

Question 2

Find the least common multiple (LCM) of $27$, $88$, and $162$.

Accepted Answer

$2376$

Question 3

Write $\frac{4}{3}$ with a denominator of $16$.

Accepted Answer

$\frac{21}{16}$

Question 4

Reduce the fraction $\frac{35}{70}$, if possible.

Accepted Answer

$\frac{1}{2}$

Question 5

Evaluate the expression: $10 - (-5) + 2 - (-10)$. Write your answer in lowest terms.

Accepted Answer

$27$

Question 6

Simplify the expression: $\sqrt{64}$.

Accepted Answer

$8$

Question 7

Simplify the radical: $\sqrt{121}$.

Accepted Answer

$11$

Question 8

Evaluate the expression: $-17 - 8 - (-4)$.

Question 9

Simplify the expression: $\frac{a^5b^7}{a^2b^3}$, assuming all variables are nonzero.

Accepted Answer

$a^3b^4$

Question 10

Use the negative exponent rule to simplify: $\left( \frac{a^2}{b^3} \right)^{-2}$, assuming all variables are nonzero.

Accepted Answer

$\frac{b^6}{a^4}$

Question 11

Solve the equation: $2x + 5 = 13$.

Accepted Answer

$x = 4$

Question 12

Determine the degree of the polynomial $2x^5 + 4x^4$.

Accepted Answer

$5$

Question 13

Factor the trinomial completely: $x^2 + 5x + 6$.

Accepted Answer

$(x + 2)(x + 3)$

Question 14

Find the greatest common factor (GCF) of $10m^3$, $40m^7$, and $10m^4$.

Accepted Answer

$10m^3$

Question 15

A chemist needs to dilute a $50\%$ acid solution to a $20\%$ acid solution by adding water. If she starts with $100$ mL of the $50\%$ solution, how much water should she add?

Accepted Answer

$150$ mL

Question 16

A patient is prescribed a medication that requires $2$ mg per kg of body weight. If the patient weighs $70$ kg, how many mg of medication are needed?

Accepted Answer

$140$ mg

Question 17

A rectangular garden has a length of $2x + 3$ meters and a width of $x - 1$ meters. What is the area of the garden in terms of $x$?

Accepted Answer

$2x^2 + x - 3$

Question 18

If $f(x) = 2x^2 - 3x + 4$, what is $f(-2)$?

Accepted Answer

$18$

Question 19

Which of the following is a solution to the equation $x^2 - 4 = 0$?

Accepted Answer

$x = 2$

Question 20

A car rental company charges a flat fee of $\$25$ plus $\$0.20$ per mile driven. If a customer paid $\$65$, how many miles did they drive?

Accepted Answer

$200$ miles

College Algebra Study Guide: Number Theory, Exponents, Polynomials, and Factoring

Study Guide - Practice Questions

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