Corollary

If p is an irreducible polynomial and b₁ , ..., b_s are polynomials such that

p | b₁ ··· b_s,

then there is an index i {1, ..., s} with p | b_i.

Unique factorization

Every nonconstant polynomial f R[X] can be written as the product of a finite number of irreducible polynomials:

f = p₁ ··· p_s,   for some positive integer s, and p_i irreducible (i = 1, ..., s).

This way of writing is unique up to the order of the irreducible factors and up to multiplication by constants.