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

Accepted Answer

$$\dfrac{5m^5$n^4$$}{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: $$\dfrac{2x^3$y^2$$}{$$4x^2y$$}$, assuming all variables are nonzero.

Accepted Answer

$$\dfrac{x y}{2}$$

College Algebra: Essential Concepts, Operations, and Problem Solving

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