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.
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.
- If needed, √2 can be converted into decimal form with a calculator, resulting in 1.41421356.
About the Author
Chance E. Gartneer began writing professionally in 2008 working in conjunction with FEMA. He has the unofficial record for the most undergraduate hours at the University of Texas at Austin. When not working on his children's book masterpiece, he writes educational pieces focusing on early mathematics and ESL topics.