The process of writing a number or a polynomial as the product of its factors.For example, since x^{2} - 1 has the factors (x + 1) and (x - 1), it can be written as (x + 1)(x - 1).

Factorization is an important concept when working with quadratic equations. To solve the equation x^{2} - 4 = 0, the solutions become apparent when the equation is factorized as follows:

x^{2} - 4 = (x + 2)(x - 2)

As shown, we have either x + 2 = 0 or x - 2 = 0.

Hence, x = -2 or x = 2.