Question 1

Which of the following best describes a polynomial equation in standard form?

Accepted Answer

An equation where all terms are on one side and the other side is zero, with the polynomial written in descending powers of the variable.

Question 2

Solve the equation by factoring: $x^2 - 5x + 6 = 0$

Accepted Answer

$x = 2$ or $x = 3$

Question 3

Which of the following is the correct first step in solving the radical equation $\sqrt{x + 3} = x - 1$?

Accepted Answer

Isolate the radical and then square both sides.

Question 4

What must you always do after solving a radical equation?

Accepted Answer

Check all proposed solutions in the original equation.

Question 5

Solve the equation with rational exponents: $x^{2/3} = 9$

Accepted Answer

$x = 27$ or $x = -27$

Question 6

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 7

Solve the absolute value equation: $|2x - 5| = 7$

Accepted Answer

$x = 6$ or $x = -1$

Question 8

Which of the following is a necessary step when solving an equation involving rational exponents, such as $x^{3/4} = 8$?

Accepted Answer

Raise both sides to the reciprocal of the exponent.

Question 9

A formula models weekly television viewing time $H$ (in hours) by annual income $I$ (in thousands of dollars): $H = -0.04I + 42.1$. What is the annual income for $H = 33.1$?

Accepted Answer

$I = 225$

Question 10

Which of the following best describes an extraneous solution?

Accepted Answer

A solution that does not satisfy the original equation after checking.

Question 11

Solve the equation: $\sqrt{2x + 3} = x$

Accepted Answer

$x = 3$

Question 12

Which of the following is the correct way to rewrite $|x| = 7$ without absolute value bars?

Accepted Answer

$x = 7$ or $x = -7$

Question 13

If $x^2 = 16$, what are the solutions?

Accepted Answer

$x = 4$ or $x = -4$

Question 14

Which of the following is a step in solving a polynomial equation by factoring?

Accepted Answer

Set each factor equal to zero and solve.

Question 15

Solve the equation: $x^{1/2} = 5$

Accepted Answer

$x = 25$

College Algebra Chapter 1.6: Other Types of Equations - Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards