Question 1

Solve the equation by factoring: $$4x^4$$ = $$12x^2. $$What are all real solutions?

Accepted Answer

$$x = 0, x = \pm \sqrt{3}$$

Question 2

Which of the following is the correct first step to solve the equation $$2x^3$$ + $$3x^2 - 8x - 12 = 0$ by factoring?

Accepted Answer

Group as $$(2x^3$$ + $$3x^2) + (-8x - 12$$)$$

Question 3

Solve the radical equation $$\sqrt{x+3} + 3 = x. $$Which of the following is a valid solution?

Accepted Answer

$$x = 4$$

Question 4

When solving a radical equation, why is it important to check for extraneous solutions?

Accepted Answer

Because squaring both sides can introduce solutions that do not satisfy the original equation.

Question 5

Solve the equation with rational exponents: $$5x^{3/2} - 25 = 0$. What is the solution?

Accepted Answer

$$x = 5$$

Question 6

Which of the following correctly expresses $$x^{m/n} in $$radical form?

Accepted Answer

$$x^{m/n}$$ = \sqrt[n]{x^m}$$

Question 7

Solve the equation $$x^{2/3} - 8 = -4$. What is the solution?

Accepted Answer

$$x = 27$$

Question 8

Which substitution would you use to solve the equation $$x^4$$ - $$8x^2 - 9 = 0$ as a quadratic in form?

Accepted Answer

Let $$u = x^2$

Question 9

Solve the equation $$3x^4$$ - $$11x^2 - 4 = 0$ by substitution. What are all real solutions?

Accepted Answer

$$x = \pm 2, x = \pm \frac{1}{\sqrt{3}}$$

Question 10

Solve the absolute value equation $$4|1-2x| - 20 = 0. $$What are the solutions?

Accepted Answer

$$x = -2.5, x = 1.5$$

Question 11

Which of the following best describes the meaning of $$|x| = 3$$?

Accepted Answer

$$x is 3 $$units away from 0 on the number line, so $$x = 3 or$$ $$x = -3$$

Question 12

A chemist is solving $$x^{2/3} - 34 = 12$ to find the concentration of a solution. What is the first step?

Accepted Answer

Add 34 to both sides

Question 13

Which of the following is a correct step in solving $$x^{3/4} - 6 = 0$?

Accepted Answer

Add 6 to both sides to isolate $$x^{3/4}$$

Question 14

If $$|x - 5| = 7$$, what are the solutions for $$x$$?

Accepted Answer

$$x = 12 or$$ $$x = -2$$

Question 15

A medical researcher models a drug's effect with $$x^{1/3} + 4 = 1$. What is the solution for x$?

Accepted Answer

$$x = -27$$

Question 16

Solve the equation $$x^3$$ + $$x^3 - 4x - 4 = 0$ by factoring. What are the solutions?

Accepted Answer

$$x = 1, x = -1, x = 2, x = -2$$

Question 17

Which of the following is the correct way to split $$|4x - 1| = 15$$ into two equations?

Accepted Answer

$$4x - 1 = 15$$ and $$4x - 1 = -15$$

Question 18

Solve the equation $$x^{2/3}$$ - $$5x^{1/3} + 6 = 0$ by substitution. What are the solutions?

Accepted Answer

$$x = 1, x = 8$$

Question 19

A biologist solves $$x^{1/2} = 9$ to find the area of a square petri dish. What is the solution for x$?

Accepted Answer

$$x = 81$$

Solving Advanced Equations in College Algebra

Study Guide - Practice Questions