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.
Calculating Square Roots
Factoring the Polynomial
Solving the Equation
If needed, √2 can be converted into decimal form with a calculator, resulting in 1.41421356.
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
Set each expression in parentheses equal to 0, then solve. The first expression set to 0 yields
The second expression set to 0 yields
The solutions for x are √2 and −√2.