Factoring is the process of breaking a number or an algebraic expression down into its smaller factor components. For example, the integer $12$ can be factored in several different ways. Similarly, multiplicative algebraic expressions, like $4x^3,$ can be rewritten in the form of a product of their coefficients and variables. The prime factorization of a multiplicative expression occurs when all of its factors are prime. This is true for both prime numbers and prime polynomials.