Let R be a field and let f, g, h be polynomials in R[X].

Lemma


Two polynomials f and g (not both zero) are relatively prime if and only if their exist polynomials a and b such that af + bg = 1.

Compare the next theorem and corollary with the results from Section 1.2 and Section 1.4.

Theorem


If f and g are relatively prime, then

f | gh   implies   f | h.