Sentence:  We claim that every <WSD>primitive polynomial</WSD> can be written as a product of irreducible elements in \mathbf D[x]....By induction on the degree of the <WSD>primitive polynomials</WSD>, we conclude that both g(x), h(x) can be written as product of irreducible elements in \mathbf D[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.