Lemma 45.26 states that if D is a UFD with a field of quotients F, then a nonconstant irreducible f(x) of D[x] is also an irreducible of F[x ]. Show by an example that a g(x) ∈ D[x] that is an irreducible of F[x] need not be an irreducible of D[x].

Data from Lemma 45.26

If D is a UFD, then a finite product of primitive polynomials in D[x] is again primitive. 

Proof This corollary follows from Lemma 45.25 by induction.