Question 1

Determine the domain of the expression $$\frac{x}{x+57}. $$Which of the following correctly describes the domain?

Accepted Answer

All real numbers except $$x = -57$$

Question 2

Reduce the rational expression $$\frac{x^2$ + 3x}{3x + 9} to $$lowest terms.

Accepted Answer

$$\frac{x}{3}$$

Question 3

Simplify the expression $$\frac{x^7$ y^3$}{x^5$ y^6$}$$, assuming all variables are nonzero.

Accepted Answer

Question 4

Reduce the rational expression $$\frac{4t - 12}{t^2$ - 9} to $$lowest terms.

Accepted Answer

$$\frac{4}{t+3}$$

Question 5

Factor the polynomial $$x^2 - 14x + 48$. Which of the following is correct?

Accepted Answer

$$(x - 8)(x - 6)$$

Question 6

Which of the following graphs best represents the solution set for $$x \geq -2 on $$the real number line?

Accepted Answer

A ray starting at $$-2$$ and extending to the right

Question 7

Factor the trinomial $$x^2 - x - 30$. Which of the following is correct?

Accepted Answer

$$(x + 5)(x - 6)$$

Question 8

Simplify the expression $$8^1$$ \cdot $$8^{-3}. $$What is the result?

Accepted Answer

$$\frac{1}{64}$$

Question 9

Multiply the polynomials $$(4x - 6)(x + 12)$$ using the FOIL method. Express your answer in standard form.

Accepted Answer

$$4x^2 + 42x - 72$

Question 10

Add the polynomials $$x^2 - 2x + 8$ and 3x^2$ + x - 6. $$Express your answer in standard form.

Accepted Answer

$$7x^2 + x - 10$

Question 11

Using synthetic division, what is the quotient and remainder when $$x^3$$ + $$3x^2 - 3x + 7$ is divided by x - 3$?

Accepted Answer

Quotient: $$x^2 + 6x + 15$, Remainder: 52$

Question 12

Factor the difference of squares $$25x^2 - 9$. Which of the following is correct?

Accepted Answer

$$(5x + 3)(5x - 3)$$

Question 13

A pharmaceutical company needs to simplify the expression $$\frac{a^4$ b^2$}{a^2$ b^5$} to $$determine the concentration of a compound. What is the simplified form?

Accepted Answer

$$a^2$$ $$b^{-3}$$

Question 14

A chemical reaction produces a compound whose concentration is modeled by $$C(t) = 4t - 12$$ and the total volume is $$V(t) = t^2$ - 9. $$What is the simplified concentration per unit volume?

Accepted Answer

$$\frac{4}{t+3}$$

Question 15

A medical dosage formula is $$D(x) = \frac{x^2$ + 3x}{3x + 9}. $$What is the lowest terms expression for the dosage?

Accepted Answer

$$\frac{x}{3}$$

Question 16

A population model is given by $$P(x) = x^2$ - x - 30. $$What are the possible values of $$x$$ for which $$P(x) = 0$$?

Accepted Answer

$$x = -5 or$$ $$x = 6$$

Question 17

A company needs to multiply $$(4x - 6) by$$ $$(x + 12) to $$determine the cost function. What is the expanded form?

Accepted Answer

$$4x^2 + 42x - 72$

Question 18

A scientist needs to simplify $$8^1$$ \cdot $$8^{-3} to $$calculate the concentration of a solution. What is the result?

Accepted Answer

$$\frac{1}{64}$$

College Algebra Practice Test Guidance

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