How to Factor X Squared Minus 2

How to Factor X Squared Minus 2
••• Sarawutnam/iStock/GettyImages

Depending on its order and the number of possessed terms, polynomial factorization can be a lengthy and complicated process. The polynomial expression, (​x2 − 2), is fortunately not one of those polynomials. The expression (​x2 − 2) is a classic example of a difference of two squares. In factoring a difference of two squares, any expression in the form of (​a2 − ​b2) is reduced to (​a​ − ​b​)(​a​ + ​b​). The key to this factoring process and ultimate solution for the expression (​x2 − 2) lies in the square roots of its terms.

    Calculate the square roots for 2 and ​x2. The square root of 2 is √2 and the square root of ​x2 is ​x​.

    Write the equation


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

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

    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.


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