 Gauss's lemma for polynomials states that the product of primitive polynomials (with coefficients in the same unique factorization domain) also is primitive.This implies that the content and the primitive part of the product of two polynomials are, respectively, the product of the contents and the product of the primitive parts.As the computation of greatest common divisors is generally much easier than polynomial factorization, the first step of a polynomial factorization algorithm is generally the computation of its primitive part–content factorization (see ).