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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