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.
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.
Write the equation x^2 -2 as the difference of two squares employing the terms' square roots. The expression x^2 -2 becomes (x - √2) (x + √2).
Set each expression in parentheses equal to 0, then solve. The first expression set to 0 yields x - √2 = 0, therefore x = √2. The second expression set to 0 yields x + √2 = 0, therefore x = -√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.