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