Question 1

Which of the following is the result of simplifying $$ (x^2$ - 3x + 2) - (x - 4x^2$) $$?

Accepted Answer

$$5x^2 - 4x + 2$

Question 2

What is the expanded form of $$ (6r - 5)^2$ $$?

Accepted Answer

$$36r^2 - 60r + 25$

Question 3

Which of the following is the correct result of $$ (t + 2)(3t^2$ - t + 4) $$?

Accepted Answer

$$3t^3$$ + $$5t^2 + 2t + 8$

Question 4

Divide $$ \frac{2x^3$ - 11x^2$ + 28}{x - 5} $$ using synthetic division. What is the quotient?

Accepted Answer

$$2x^2 - x - 5$$ + \frac{3}{x-5}$$

Question 5

What is the result of $$ \frac{3x^3$ + 4x^2$ - 9x + 6}{x + 2} $$ using synthetic division?

Accepted Answer

$$3x^2 - 2x - 5$$ + \frac{16}{x+2}$$

Question 6

Factor completely: $$6x^2 - 17x + 7$

Accepted Answer

$$(3x - 7)(2x - 1)$$

Question 7

Factor completely: $$x^4 - 16$

Accepted Answer

$$(x - 2)(x + 2)(x^2$ + 4)$$

Question 8

Solve for $$x$$: $$|x + 4| = 7$$

Accepted Answer

$$x = 3 or$$ $$x = -11$$

Question 9

Solve for $$x$$: $$|2 - x| = 3$$

Accepted Answer

$$x = -1 or$$ $$x = 5$$

Question 10

Solve for $$x$$: $$\left| \frac{7}{2 - 3x} \right| - 9 = 0$$

Accepted Answer

$$x = \frac{2}{3} \pm \frac{7}{18}$$

Question 11

Solve for $$x$$: $$3(x - 4) - 5(x + 2) = 2 - (x + 24)$$

Accepted Answer

$$x = -5$$

Question 12

Given the quadratic function $$f(x) = -2x^2$ + 6x - 3$$, what is the vertex of the parabola?

Accepted Answer

$$(1.5, 1.5)$$

Question 13

A small rocket is fired vertically upward, and its height after $$t$$ seconds is given by $$h(t) = -16t^2$ + 88t + 48. At $$what time does the rocket reach its maximum height?

Accepted Answer

$$t = 2.75$$ seconds

Question 14

Which of the following is the correct factorization of $$24m^3$$ - $$14m^2 - 24m$?

Accepted Answer

$$2m(12m^2 - 7m - 12$$)$$

Question 15

Solve for $$x$$: $$6x^2 - 11x - 7 = 0$

Accepted Answer

$$x = 7/6, x = -1$$

Question 16

Which of the following is the correct simplification of $$\frac{x}{x^2$ + 3x + 2} + \frac{2x}{2x^2$ - x - 3}$$?

Accepted Answer

$$\frac{3x}{(x+1)(x+2)(2x-3)}$$

Question 17

Which of the following is the correct result of $$\frac{5x^2$ - 9x - 2}{30x^3$ + 6x^2$} \div \frac{x^4$ - 3x^2$ - 4}{2x^8$ + 6x^7$ + 4x^6$}$$?

Accepted Answer

$$\frac{(5x^2$ - 9x - 2)(2x^8$ + 6x^7$ + 4x^6$)}{(30x^3$ + 6x^2$)(x^4$$ - $$3x^2 - 4$$)}$

College Algebra Study Guide: Operations, Factoring, Equations, and Applications

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