Factoring X Squared Minus 2

Published
<h3>Factoring X Squared Minus 2</h3>

Depending on its order and the number of possessed terms, polynomial factorization can be a lengthy and complicated process. The polynomial expression, (​x​2 − 2), is fortunately not one of those polynomials. The expression (​x​2 − 2) is a classic example of a difference of two squares. In factoring a difference of two squares, any expression in the form of (​a​2 − ​b​2) is reduced to (​a​ − ​b​)(​a​ + ​b​). The key to this factoring process and ultimate solution for the expression (​x​2 − 2) lies in the square roots of its terms.

1. Calculating Square Roots

Calculate the square roots for 2 and ​x​2. The square root of 2 is √2 and the square root of ​x​2 is ​x​.

2. Factoring the Polynomial

Write the equation



((x^2-2))

as the difference of two squares employing the terms’ square roots. You find that

((x^2-2) = (x-sqrt{2}) (x+sqrt{2}))

3. Solving the Equation

Set each expression in parentheses equal to 0, then solve. The first expression set to 0 yields



((x-sqrt{2})=0 text{ therefore } x= sqrt{2})

The second expression set to 0 yields

((x+ sqrt{2}) = 0 text{ therefore } x=- sqrt{2})



The solutions for ​x​ are √2 and −√2.

TL;DR (Too Long; Didn’t Read)

If needed, √2 can be converted into decimal form with a calculator, resulting in 1.41421356.

Dave Pennells

By Dave Pennells

Dave Pennells, MS, has contributed his expertise as a career consultant and training specialist across various fields for over 15 years. At City University of Seattle, he offers personal career counseling and conducts workshops focused on practical job search techniques, resume creation, and interview skills. With a Master of Science in Counseling, Pennells specializes in career consulting, conducting career assessments, guiding career transitions, and providing outplacement services. Her professional experience spans multiple sectors, including banking, retail, airlines, non-profit organizations, and the aerospace industry. Additionally, since 2001, he has been actively involved with the Career Development Association of Australia.