UFD? Nature of polynomial x in the Ring Q_Z[x]

Let denote the set of polynomials with rational coefficients and integer constant terms.

(a) Show that the only divisors of x in are the integers (constant polynomials) and first degree polynomials of the form with

(b) For each non-zero show that the polynomial is not irreducible in

(c) Show that x cannot be written as a finite product of irreducible elements in

Would appreciate help with this exercise

Peter

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Re: UFD? Nature of polynomial x in the Ring Q_Z[x]

Hi again,

This continues the problem of your previous posting. What this does is prove the ring in question is not a unique factorization domain. Here's a solution:

Attachment 28399