primitive polynomial

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

Primitive polynomials make the initialization of LFSRs a simpler task since any nonzero state guarantees that all non-zero states will be visited in the maximum length sequence.