Question 1

Solve the equation $$2x^2 - 2 = 30$ by taking square roots.

Accepted Answer

$$x = \pm 4$$

Question 2

Which of the following is the solution to $$3x^2 + 3 = 36$?

Accepted Answer

$$x = \pm \sqrt{11}$$

Question 3

Solve $$5x^2$$ - $$5x^2 = -40$ by taking square roots.

Accepted Answer

No solution

Question 4

What is the solution to $$3x^2 + 3x = -48$?

Accepted Answer

$$x = \frac{-3 \pm \sqrt{597}}{6}$$

Question 5

Solve $$x^2 + 14x + 83 = -7$ by completing the square.

Accepted Answer

$$x = -7 \pm \sqrt{56}$$

Question 6

Which of the following is the solution to $$x^2 + 20x + 91 = -8$ by completing the square?

Accepted Answer

$$x = -10 \pm \sqrt{183}$$

Question 7

Solve $$x^2 - 16x - 66 = -5$ by completing the square.

Accepted Answer

$$x = 8 \pm \sqrt{135}$$

Question 8

Simplify the sum $$6m - 2m^2$ + 6m^3$ + (4m^3$ - 7m - 2m^2$) + (6m^2$ - 2).$$

Accepted Answer

$$10m^3$$ + $$2m^2 - m - 2$

Question 9

Simplify the difference $$(4m^2 - 7$$ - $$4m^3) - (3$$ + $$m^2$$ - $$4m^3) - (6m$$ - $$6m^3$$)$$.

Accepted Answer

$$-6m^3$$ + $$3m^2 - 6m - 10$

Question 10

Simplify $$(a - 6a^2$ - 5a) - (5a + 2a^2$ - a^3$) - (5 - 8a^3$).$$

Accepted Answer

$$-9a^3$$ - $$8a^2 - 9a - 5$

Question 11

Find the product $$(x + 7)(x + 5).$$

Accepted Answer

$$x^2 + 12x + 35$

Question 12

Find the product $$(3x + 3)(6x + 3).$$

Accepted Answer

$$18x^2 + 27x + 9$

Question 13

Find the product $$(5x + 2)(2x^2$ - 8x - 2).$$

Accepted Answer

$$10x^3$$ - $$36x^2 - 14x - 4$

Question 14

Find the product $$(6x + 2)(2x^2$ + 2x + 7).$$

Accepted Answer

$$12x^3$$ + $$16x^2 + 46x + 14$

Question 15

A biologist is modeling the population growth of a species using the quadratic equation $$P(t) = t^2$ + 14t + 83. If $$the population drops to $$-7$$, what is the value of $$t$$?

Accepted Answer

$$t = -7 \pm \sqrt{56}$$

Question 16

A chemical reaction's rate is modeled by $$R(x) = x^2$ + 20x + 91. If $$the rate decreases to $$-8$$, what is the value of $$x$$?

Accepted Answer

$$x = -10 \pm \sqrt{183}$$

Question 17

A medical researcher uses the equation $$x^2 - 16x - 66 = -5$ to model the spread of a virus. What are the possible values of x$?

Accepted Answer

$$x = 8 \pm \sqrt{135}$$

College Algebra Pretest Review: Equations, Simplification, and Polynomial Operations

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