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

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

Accepted Answer

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

Question 4

Evaluate $$| -183 |.$$

Accepted Answer

$$183$$

Question 5

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

Accepted Answer

$$14$$

Question 6

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

Accepted Answer

$$-3$$

Question 7

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

Accepted Answer

$$5\sqrt{2}$$

Question 8

Evaluate $$-4^2.$$

Accepted Answer

$$-16$$

Question 9

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

Accepted Answer

$$-15z^6$$

Question 10

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

Accepted Answer

$$4m^4n^3$

Question 11

Use the negative exponent rule to simplify $$11^{-2}$$ and write the answer with positive exponents.

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

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

Accepted Answer

$$x = -24$$

Question 14

Which of the following is the degree of the polynomial $$2x^5$$ + $$7x^4 - 5x$?

Accepted Answer

$$5$$

Question 15

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

Accepted Answer

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

Question 16

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

Accepted Answer

$$20m^3$$

Question 17

A chemist mixes two solutions: one with $$3x^2 - 5x + 12$ grams of chemical A$ and another with x = 3$. How many grams of chemical A$ are in the mixture?

Accepted Answer

$$24$$

Question 18

Simplify $$-13xy \div -3xy^2$ and write the answer with positive exponents.

Accepted Answer

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

Question 19

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

Accepted Answer

$$x(x + 3)^2$

Question 20

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$

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

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