Question 1

Which of the following is the correct first step when solving a quadratic equation by factoring?

Accepted Answer

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

Question 2

Solve the equation $$x^2 = 25x$ by factoring.

Accepted Answer

$$x = 25 or$$ $$x = 0$$

Question 3

Given $$3x^2 - 2 = 5x$, what are the solutions for x$ after factoring?

Accepted Answer

$$x = -\frac{1}{3}$$, x = 2$

Question 4

Which of the following is a necessary step when solving $$x^2 + 4x - 2 = 0$ by factoring?

Accepted Answer

Express the quadratic in standard form and factor.

Question 5

If $$x^2 + 4x - 2 = 0$ is factored as (x-2)(x+1) = 0$, what are the solutions?

Accepted Answer

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

Question 6

A chemical reaction's rate is modeled by $$x^2 - 25x = 0$. What are the possible values for x$ (rate) if x$ must be non-negative?

Accepted Answer

$$x = 0 or$$ $$x = 25$$

Question 7

Which of the following equations is equivalent to $$x^2 + 4x - 2 = 0$ after moving all terms to one side?

Accepted Answer

$$x^2 + 4x - 2 = 0$

Question 8

A business's profit is modeled by $$3x^2 - 2 = 5x$. What are the possible values for x$ (in thousands of units sold) after solving by factoring?

Accepted Answer

$$x = -\frac{1}{3} or$$ $$x = 2$$

Question 9

Which of the following is NOT a valid step in solving a quadratic equation by factoring?

Accepted Answer

Multiply both sides by zero.

Question 10

If $$x^2 + 4x - 2 = 0$ models the height (in meters) of a projectile, what are the possible times (in seconds) when the projectile is at height zero?

Accepted Answer

$$x = 2 or$$ $$x = -1$$

Question 11

Which of the following best describes the Zero Product Property used in factoring?

Accepted Answer

If $$ab = 0$$, then $$a = 0 or$$ $$b = 0.$$

Question 12

Which equation is correctly set up for factoring after moving all terms to one side: $$3x^2 - 2 = 5x$?

Accepted Answer

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

Factoring and Solving Quadratic Equations: College Algebra Lesson 1.3 Study Notes

Study Guide - Practice Questions