Question 1

Which of the following is the correct prime factorization of $$294$$?

Accepted Answer

$$2 \cdot 3 \cdot 7 \cdot 7$$

Question 2

What is the least common multiple (LCM) of $$8$$, $$18$$, and $$24$$?

Accepted Answer

$$72$$

Question 3

Simplify the expression $$\sqrt{16} + \sqrt{100}.$$

Accepted Answer

$$14$$

Question 4

Evaluate $$|4 - 12| \cdot 3 \div (-6).$$

Accepted Answer

$$-4$$

Question 5

Which of the following is the simplified form of $$(3z^4)(-5z^2$)$?

Accepted Answer

$$-15z^6$$

Question 6

Simplify the expression $$\dfrac{40m^6$n^7$$}{$$10m^2n^4$}.$$

Accepted Answer

$$4m^4n^3$

Question 7

Use the negative exponent rule to simplify $$\left(\dfrac{3}{8}\$$right)^{-2}$$.

Accepted Answer

$$\dfrac{64}{9}$$

Question 8

Which of the following is the correct simplification of $$(-3x^4y$$^{-3}$$)(8x^{-2}y$$)$$ with positive exponents?

Accepted Answer

$$-24x^2y^2$

Question 9

Solve for $$x in $$the equation $$\dfrac{x}{x+12} = \dfrac{3}{5}.$$

Accepted Answer

$$x = -9$$

Question 10

What is the degree of the polynomial $$2x^9$$ + $$7x^4 - 5x$?

Accepted Answer

$$9$$

Question 11

Factor the trinomial $$x^2 - x - 20$ completely.

Accepted Answer

$$(x - 5)(x + 4)$$

Question 12

Which of the following is the greatest common factor (GCF) of $$20m^7$$, $$40m^3$$, and $$80m^9$$?

Accepted Answer

$$20m^3$$

Question 13

A chemist needs to mix two solutions. One contains $$x$$ grams of salt, and the other contains $$x+12$$ grams. If the ratio of salt in the first to the second must be $$3:5$$, how many grams of salt should be in the first solution?

Accepted Answer

$$-9$$ grams

Question 14

Simplify $$\left(\dfrac{3m$$^{-2}$$n^4$$}{$$m^3n^2$}\$$right)^{-2}$$ and write the answer with positive exponents.

Accepted Answer

$$\dfrac{m^2$}{9n^4$}$$

Question 15

Factor the expression $$x^3$$ + $$6x^2 + 9x$ completely.

Accepted Answer

$$x(x + 3)^2$

Question 16

A rectangular garden has a length of $$2x + 4$$ meters and a width of $$4x - 7$$ meters. What is the area of the garden in terms of $$x$$?

Accepted Answer

$$8x^2 + 2x - 28$

Question 17

Which of the following is the simplified form of $$\dfrac{-13xy}{-3xy^2$}$$?

Accepted Answer

$$\dfrac{13}{3y}$$

Question 18

Evaluate $$(2x - 3y)^2$ for x = 7$ and y = -2$.

Accepted Answer

$$400$$

Question 19

Which of the following is the correct factorization of $$x^2 - 49$?

Accepted Answer

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

Question 20

A company’s profit $$P (in $$thousands of dollars) is modeled by $$P = 3x^2$ - 5x + 12$$, where $$x is $$the number of units sold (in hundreds). What is the profit when $$x = 3$$?

Accepted Answer

$$24$$

Comprehensive Step-by-Step Guidance for Beginning-Intermediate Algebra Review

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