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 (x2-2) as the difference of two squares employing the terms' square roots. The expression (x2-2) 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.