Question 1

Factor the following expression completely: $$8x^2y^3$ + 10xy^2$ - 18xy$

Accepted Answer

$$2xy(4xy^2 + 5y - 9$$)$$

Question 2

Which of the following is the correct complete factorization of $$100z^3 - 121$?

Accepted Answer

Question 3

Factor the following trinomial completely: $$x^2 + 6x - 16$

Accepted Answer

$$(x + 8)(x - 2)$$

Question 4

Which value of $$x$$ makes the expression $$\dfrac{1}{x^2$ - 4}$$ undefined?

Accepted Answer

$$x = 2 or$$ $$x = -2$$

Question 5

Simplify the rational expression $$\dfrac{75m^2$ - 3}{25m - 5} to $$lowest terms.

Accepted Answer

Question 6

Find all real solutions to the equation $$x^2 - 16 = 9$.

Accepted Answer

$$x = 5, x = -5$$

Question 7

A rational expression is undefined for which value(s) of $$x$$? $$\dfrac{4x^2$ + 3x + 4}{5x^2$ + 4x + 4}$$

Accepted Answer

$$x$$ such that $$5x^2 + 4x + 4 = 0$

Question 8

Simplify the complex fraction: $$\dfrac{\dfrac{2}{m^2$} - \dfrac{1}{8}}{\dfrac{1}{7} - \dfrac{1}{64}}$$

Accepted Answer

$$\dfrac{16(m^2$ - 8)}{7(m^2$ - 8)}$$

Question 9

Trevor Bayne drove 500 miles in 3.836 hours. What was his average speed, rounded to the nearest thousandth?

Accepted Answer

$$130.344$$ mph

Question 10

Solve for $$x$$: $$6x^2 - 15x - 9 = 0$

Accepted Answer

$$x = 3, x = -1/2$$

Question 11

Which of the following is the correct factorization for $$64x^3 - 125$?

Accepted Answer

$$(4x - 5)(16x^2$ + 20x + 25)$$

Question 12

Given $$\dfrac{11x^2$ + 6x + 11}{2x^2$ + 6x + 4}$$, find its value when $$x = 2.$$

Accepted Answer

$$\dfrac{28}{24}$$

Question 13

Which of the following is the correct simplification of $$\dfrac{v^2$ - 4}{v - 2}$$?

Accepted Answer

$$v + 2$$

Question 14

Solve for $$x$$: $$\dfrac{7}{x - 2} - \dfrac{17}{x - 5} = 2$$

Accepted Answer

$$x = 7$$

Question 15

Which of the following is the correct factorization for $$7x^2 - 21x - 70$?

Accepted Answer

$$7(x - 7)(x + 10)$$

Question 16

Which of the following is the correct simplification of $$\dfrac{4x^2$ - 1}{2x - 2}$$?

Accepted Answer

Question 17

Solve for $$y$$: $$\dfrac{y^2$ - 12}{6y - 6} = \dfrac{144}{y^2$ - 36}$$

Accepted Answer

No solution

Question 18

Which of the following is the correct factorization for $$10x^2 + 55x + 70$?

Accepted Answer

$$5(2x + 7)(x + 2)$$

Question 19

Which of the following is the correct simplification of $$\dfrac{a^2$ - 1}{a - 1}$$?

Accepted Answer

$$a + 1$$

Question 20

Which of the following is the correct factorization for $$4x^3$$ + $$3x^2 - 10x$?

Accepted Answer

$$x(4x^2 + 3x - 10$$)$$

MTH 100 Chapter 5 & 6 Test Review – Step-by-Step Algebra Guidance

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