Sentence:  According to the Gauss lemma, the product of <WSD>primitive polynomials</WSD> is primitive. Therefore if f(x), g(x) are primitive and f(x)=g(x)h(x) with h(x) in F[x], then necessarily h(x) is in A[x] and primitive. ...The irreducible elements of A[x] are irreducible elements of A and <WSD>primitive polynomials</WSD> which are irreducible in F[x]. 
Meaning of the word marked with <WSD> tags:  A polynomial over an integral domain "R" such that no noninvertible element of "R" divides all its coefficients at once;  a polynomial over a GCD domain "R" such that the greatest common divisor of its coefficients equals 1.