Question 1

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

Accepted Answer

$2 	imes 3^2 	imes 7$

Question 2

A chemist needs to prepare solutions in containers of $27$, $88$, and $162$ mL. What is the least common multiple (LCM) of these volumes so that each container can be filled an exact number of times?

Accepted Answer

$4752$

Question 3

Reduce the fraction $\dfrac{35}{70}$ to lowest terms.

Accepted Answer

$\dfrac{1}{2}$

Question 4

Evaluate the expression: $-2 	imes (-5) 	imes (-6)$.

Accepted Answer

$-60$

Question 5

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

Accepted Answer

$11$

Question 6

A square garden has an area of $64$ square meters. What is the length of one side?

Accepted Answer

$8$ meters

Question 7

Simplify the expression: $\dfrac{5m^7n^8}{4m^2n^4}$, assuming all variables are nonzero.

Accepted Answer

$\dfrac{5m^5n^4}{4}$

Question 8

Use the negative exponent rule to simplify: $\left( \dfrac{a^3}{b^2} \right)^{-2}$, where $a$ and $b$ are nonzero.

Accepted Answer

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

Question 9

Which of the following is the degree of the polynomial $2x^5 + 4x^4$?

Accepted Answer

$5$

Question 10

Factor the trinomial $x^2 + 3x - 4$ completely.

Accepted Answer

$(x + 4)(x - 1)$

Question 11

A rectangular field has a length of $2x + 5$ meters and a width of $x$ meters. What is the area of the field in terms of $x$?

Accepted Answer

$2x^2 + 5x$

Question 12

Solve for $x$: $2x - 7 = 15$.

Accepted Answer

$x = 11$

Question 13

Which of the following is the greatest common factor (GCF) of $10m^3$, $40m^7$, and $100m^4$?

Accepted Answer

$10m^3$

Question 14

A biologist is studying the population growth of bacteria, which triples every hour. If the initial population is $P_0$, what is the population after $n$ hours?

Accepted Answer

$P_0 	imes 3^n$

Question 15

Simplify the expression: $(-2)^3 \cdot (-4)^2$.

Accepted Answer

$-128$

Question 16

If $x = 6$ and $y = 8$, evaluate $x^2 + y^2$.

Accepted Answer

$100$

Question 17

Which of the following is a solution to the equation $3x + 1 = x + 5$?

Accepted Answer

$x = 2$

Question 18

Factor the trinomial $x^2 - 2x - 35$ completely.

Accepted Answer

$(x - 7)(x + 5)$

Question 19

A pharmacist needs to mix two solutions: one with $20\%$ concentration and one with $50\%$ concentration to obtain $100$ mL of a $30\%$ solution. Which equation represents the amount $x$ (in mL) of the $20\%$ solution needed?

Accepted Answer

$0.2x + 0.5(100 - x) = 30$

Question 20

Simplify the expression: $\dfrac{2x^3y^2}{4x^2y}$, assuming all variables are nonzero.

Accepted Answer

$\dfrac{x y}{2}$

College Algebra: Essential Concepts, Operations, and Problem Solving

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