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Mini-Quiz: Solving Quadratic Equations by Factoring

by Ron Kurtus (updated 18 January 2022)

Take this Mini-Quiz to check your understanding of the lesson material.

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1. How do you solve (x − 5)(x + 7) = 0?

The equation cannot be solved

Set (x − 5) = 0 and (x + 7) = 0 and solve each for x

x = −5 + 7

2. What is the solution of the equation x² − 25 = 0?

x = 25

You cannot factor an equation with a negative number

x = 5 and x = −5

3. Why can't you solve x² + x + 1 = 0 by factoring?

The expression x² + x + 1 cannot be factored with rational numbers

You can solve it by factoring, since: (x +1)(x + 1) = 0

The expression x² + x + 1 cannot equal 0

If you got all three correct, you are on your way to becoming a Champion in Algebra. If you had problems, you had better look over the material again.

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Be strong

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Algebra topics

Mini-Quiz: Solving Quadratic Equations by Factoring

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Algebra topics

Basics

• Definition of Algebra
• Purpose of Algebra

Terminolgy

• Terminology Used in Algebra
• Variables and Constants
• Operations and Symbols
• Algebraic Expressions

Properties

• Addition and Multiplication
• Product of Negative Numbers
• Algebra of Objects
• Imaginary Numbers

Expressions

• Combining Like Terms
• Multiplying Binomial Expressions

Exponents and roots

• Exponents
• Exponent Rules
• Multiplication with Exponents
• Division with Exponents
• Exponents to the Power of 10
• Square Roots
• Newton's Approximation

Equations

• Linear Equations
• Solving One Variable Equation

Quadratic equations

• Quadratic Equations
• Solving Equations by Factoring
• Completing the Square Method
• Using the Quadratic Formula
• Derivation of Quadratic Formula

Also see

• Algebra Survey Results
• Arithmetic
• Physical Science
• Chemistry
• Good Grades

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