Question 1

Which of the following is the correct first step to solve the equation $$x^2 - 9x + 20 = 0$ by factoring?

Accepted Answer

Move all terms to one side to set the equation equal to zero.

Question 2

Solve the equation $$x^2 - 4 = 0$. What is the solution set?

Accepted Answer

$$\left\{2, -2\right\}$$

Question 3

Which of the following best describes a radical equation?

Accepted Answer

An equation in which the variable occurs in a root, such as a square root or cube root.

Question 4

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

Accepted Answer

$$x = 6$$

Question 5

Which of the following is an extraneous solution to the equation $$\sqrt{x + 3} + 3 = x$$?

Accepted Answer

$$x = 1$$

Question 6

Solve the equation $$5x^{\frac{2}$${3}} - 25 = 0$$ for x$.

Accepted Answer

$$x = \sqrt[3]{25}$$

Question 7

Which substitution would you use to solve the equation $$x^4$$ - $$5x^2 + 6 = 0$ as a quadratic in form?

Accepted Answer

Let $$u = x^2$

Question 8

Solve the equation $$x^4$$ - $$5x^2 + 6 = 0$. Which of the following is NOT a solution?

Accepted Answer

$$x = 0$$

Question 9

If $$|2x - 1| = 5$$, what is the solution set for $$x$$?

Accepted Answer

$$\left\{3, -2\right\}$$

Question 10

Which of the following statements about absolute value equations is correct?

Accepted Answer

If $$|u| = c$$ where $$c \u003e 0$$, then $$u = c or$$ $$u = -c.$$

Question 11

A formula for weekly TV viewing time is $$H = -2.3\sqrt{I} + 67.6$$, where $$H is $$hours and $$I is $$annual income in thousands of dollars. If $$H = 33.1$$, what is the value of $$I$$?

Accepted Answer

$$I = 225$$

Question 12

Which of the following best describes the process for solving a radical equation?

Accepted Answer

Isolate the radical, raise both sides to the appropriate power, solve, and check for extraneous solutions.

Question 13

Which of the following is a polynomial equation?

Accepted Answer

$$x^3$$ - $$2x^2 + x - 5 = 0$

Question 14

Which of the following is the degree of the polynomial equation $$4x^5$$ - $$3x^2 + 2 = 0$?

Accepted Answer

5

Question 15

Solve the equation $$x^{\frac{2}$${3}} = 9$$. What is the value of x$?

Accepted Answer

$$x = 27$$

Question 16

Which of the following is a necessary step when solving equations with rational exponents?

Accepted Answer

Raise both sides to the reciprocal of the rational exponent.

Question 17

A chemical reaction is modeled by the equation $$C^2 - 8C + 15 = 0$, where C$ is the concentration in mol/L. What are the possible concentrations?

Accepted Answer

$$C = 5 or$$ $$C = 3$$

Question 18

Which of the following is a real-world application of solving equations involving absolute value?

Accepted Answer

Finding the range of temperatures within a certain tolerance from a target value.

Solving Various Types of Equations in College Algebra

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