Question 1

Which of the following is the complete factorization of $$3x^3$$ - $$2x^2 - 6x + 4$?

Accepted Answer

Question 2

Solve the equation $$10x^3 - 40x = 0$ by factoring. Which of the following lists all real solutions?

Accepted Answer

$$x = 0, x = 2$$

Question 3

What is the domain of the rational function $$f(x) = \frac{3x}{x^2$ - 13x + 36}$$?

Accepted Answer

All real numbers except $$x = 9$$ and $$x = 4$$

Question 4

Simplify the rational expression $$\frac{x^2$ - 7x + 12}{9 - x^2$}$$ completely.

Accepted Answer

$$-\frac{(x - 3)(x - 4)}{(x + 3)(x - 3)}$$

Question 5

A company has a fixed monthly cost of $$20,000 and a variable cost of 20$ per canoe produced. What is the average cost function $$\overline{C}(x)$$ for producing x$ canoes?

Accepted Answer

$$\overline{C}(x) = \frac{20,000 + 20x}{x}$$

Question 6

How many canoes must be produced each month for the company to have an average cost of $$40 per canoe? (Fixed cost 20$$,000$$, variable cost 20$ per canoe)

Accepted Answer

$$x = 1,000$$

Question 7

Evaluate $$\sqrt{-16}. $$Which of the following is correct?

Accepted Answer

$$4i$$

Question 8

Rewrite $$(25)^{3/2}$$ using radical notation and simplify.

Accepted Answer

$$(\sqrt{25})^3$ = 125$$

Question 9

Simplify $$\sqrt{-36}$$ and express your answer in the form $$a + bi.$$

Accepted Answer

$$6i$$

Question 10

Solve the equation $$5x^2 + 9 = 29$ using the square root property. What are the solutions?

Accepted Answer

Question 11

A rectangular park is 6 miles long and 3 miles wide. How long is the diagonal route across the park? Round to the nearest tenth.

Accepted Answer

$$\sqrt{6^2$ + 3^2$} = 6.7$$ miles

Question 12

Solve $$x^2 + 6x + 13 = 0$ using the quadratic formula. Express your answer in the form a + bi$.

Accepted Answer

$$x = -3 \pm 2i$$

Question 13

For the function $$f(x) = (x + 3)^2$ - 9$$, what is the vertex?

Accepted Answer

$$(-3, -9)$$

Question 14

For the function $$f(x) = 2x^2$ - 12x + 10$$, what is the $$y-$$intercept?

Accepted Answer

$$10$$

Question 15

Consider the quadratic function $$f(x) = -3x^2$ + 12x + 1. $$Without graphing, does the function have a maximum or minimum value?

Accepted Answer

Maximum, because the leading coefficient is negative

Question 16

A person throws a baseball upward from a 200-foot building. The height is modeled by $$s(t) = -16t^2$ + 64t + 200. $$After how many seconds does the ball reach its maximum height?

Accepted Answer

$$t = 2$$ seconds

Question 17

For the function $$f(x) = \sqrt{x - 3}$$, what is the domain?

Accepted Answer

$$x \geq 3$$

Question 18

Simplify $$\left(\frac{8}{125}\$$right)^{-1/3}$$.

Accepted Answer

$$\frac{5}{2}$$

Question 19

Which of the following is the least common denominator (LCD) for $$\frac{4x}{x-2}$$ and $$\frac{x+1}{x-5}$$?

Accepted Answer

$$(x-2)(x-5)$$

College Algebra Review: Factoring, Quadratics, Rational Functions, and More

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