Question 1

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

Accepted Answer

$$2 	imes 3^2$ 	imes 7$$

Question 2

Find the least common multiple (LCM) of $$27$$, $$88$$, and $$162.$$

Accepted Answer

$$2376$$

Question 3

Write $$\frac{4}{3}$$ with a denominator of $$16.$$

Accepted Answer

$$\frac{21}{16}$$

Question 4

Reduce the fraction $$\frac{35}{70}$$, if possible.

Accepted Answer

$$\frac{1}{2}$$

Question 5

Evaluate the expression: $$10 - (-5) + 2 - (-10). $$Write your answer in lowest terms.

Accepted Answer

$$27$$

Question 6

Simplify the expression: $$\sqrt{64}.$$

Accepted Answer

$$8$$

Question 7

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

Accepted Answer

$$11$$

Question 8

Evaluate the expression: $$-17 - 8 - (-4).$$

Accepted Answer

Question 9

Simplify the expression: $$\frac{a^5$b^7$$}{$$a^2b^3$}$$, assuming all variables are nonzero.

Accepted Answer

$$a^3b^4$

Question 10

Use the negative exponent rule to simplify: $$\left( \frac{a^2$}{b^3$} \$$right)^{-2}$$, assuming all variables are nonzero.

Accepted Answer

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

Question 11

Solve the equation: $$2x + 5 = 13.$$

Accepted Answer

$$x = 4$$

Question 12

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

Accepted Answer

$$5$$

Question 13

Factor the trinomial completely: $$x^2 + 5x + 6$.

Accepted Answer

$$(x + 2)(x + 3)$$

Question 14

Find the greatest common factor (GCF) of $$10m^3$$, $$40m^7$$, and $$10m^4.$$

Accepted Answer

$$10m^3$$

Question 15

A chemist needs to dilute a $$50\%$$ acid solution to a $$20\%$$ acid solution by adding water. If she starts with $$100 mL of $$the $$50\%$$ solution, how much water should she add?

Accepted Answer

$$150 mL$$

Question 16

A patient is prescribed a medication that requires $$2 mg $$per kg of body weight. If the patient weighs $$70 kg$$, how many mg of medication are needed?

Accepted Answer

$$140 mg$$

Question 17

A rectangular garden has a length of $$2x + 3$$ meters and a width of $$x - 1$$ meters. What is the area of the garden in terms of $$x$$?

Accepted Answer

$$2x^2 + x - 3$

Question 18

If $$f(x) = 2x^2$ - 3x + 4$$, what is $$f(-2)$$?

Accepted Answer

$$18$$

Question 19

Which of the following is a solution to the equation $$x^2 - 4 = 0$?

Accepted Answer

$$x = 2$$

Question 20

A car rental company charges a flat fee of $$\25$ plus $$\$$0.20$$ per mile driven. If a customer paid $$\65$, how many miles did they drive?

Accepted Answer

$$200$$ miles

College Algebra Study Guide: Number Theory, Exponents, Polynomials, and Factoring

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