Question 1

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

Accepted Answer

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

Question 2

A chemist needs to mix chemicals in batches of $$8$$, $$18$$, and $$24$$ milliliters. What is the least common multiple (LCM) of these batch sizes?

Accepted Answer

$$72$$

Question 3

Write $$\dfrac{5}{6}$$ with a denominator of $$18.$$

Accepted Answer

$$\dfrac{15}{18}$$

Question 4

Reduce the fraction $$\dfrac{10}{14} to $$lowest terms.

Accepted Answer

$$\dfrac{5}{7}$$

Question 5

Evaluate the expression $$12 + (−4) − 3 + 8.$$

Accepted Answer

$$13$$

Question 6

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

Accepted Answer

$$14$$

Question 7

Simplify $$\sqrt[3]{-27}.$$

Accepted Answer

$$-3$$

Question 8

Use the product rule to simplify $$\sqrt{50}.$$

Accepted Answer

$$5\sqrt{2}$$

Question 9

Evaluate $$-4^2.$$

Accepted Answer

$$-16$$

Question 10

Simplify $$(3z^4)(-5z^2$)$.

Accepted Answer

$$-15z^6$$

Question 11

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

Accepted Answer

$$4m^4n^3$

Question 12

Use the negative exponent rule to simplify $$11^{-2}.$$

Accepted Answer

$$\dfrac{1}{121}$$

Question 13

Simplify $$(mn^3)^2$(2m^3n^4$)$.

Accepted Answer

$$2m^5n$$^{10}$

Question 14

Solve for $$x$$: $$9(x + 2) = 2(4x - 3).$$

Accepted Answer

$$x = -24$$

Question 15

A pharmacist needs to dilute a solution. If $$x mL of $$pure solution is added to $$12 mL of $$water, and the ratio of solution to total volume must be $$3:5$$, what is $$x$$?

Accepted Answer

$$x = -9$$

Question 16

Determine the degree of the polynomial $$2x^5$$ + $$7x^4 - 5x$.

Accepted Answer

$$5$$

Question 17

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

Accepted Answer

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

Question 18

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

Accepted Answer

$$20m^3$$

Question 19

Factor $$x^2 - 49$ completely.

Accepted Answer

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

Question 20

A rectangular garden has an area represented by $$x^2 + 12x + 36$ square meters. What are the possible dimensions of the garden?

Accepted Answer

$$(x + 6)$$ meters by $$(x + 6)$$ meters

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

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