Factorization : A factorization of a number or expression is writing the number or expression as a product of several factors. For example $12=2\cdot 2\cdot 3$ is a factorization of 12 and $x^2+2x+1=(x+1)(x+1)$ is a factorization of $x^2+2x+1.$ Factorizations of expressions are often helpful in finding roots of the initial expression as a product of several numbers is zero if and only if one of the factors is zero.