Prime factorization of a monomial involves factoring the constant part of the monomial to its prime numbers. It also factors out the variables.
- Identify and separate the factors
Separate the monomial into its individual constituents. In the case of the monomial, 12x^3y^2, the individual factors are 12, x^3 and y^2. X^3 and y^2 are both variables, and 12 is a constant.
- Break down the constant
Break down the constant into its prime factors. These are factors that cannot be broken down into real integers any further. Twelve breaks down into its factors of 3 and 4. Three is a prime number, and its only other factor is 1. Four factors out to 2 and 2. Two is a prime number. Therefore, the prime factorization of 12 is 3 * 2 * 2.
- Look at the degree of each variable
The variables x^3 and y^2 have degrees of 3 and 2, respectively. This means that the variable x^3 factors out to x * x * x and the variable y^2 factors out to y * y.
- Write out factors of monomials
Putting all the factors together gives the factorization of the given monomial. The monomial 12x^3y^2 factors out to 2 * 2 * 3 * x * x * x * y * y. If the constant is negative, place a -1 in the constant factorization.