  We investigate non-unique factorization of polynomials in Z_{p^n}[x] into
irreducibles. As a Noetherian ring whose zero-divisors are contained in the
Jacobson radical, Z_{p^n}[x] is atomic. We reduce the question of factoring
arbitrary non-zero polynomials into irreducibles to the problem of factoring
monic polynomials into monic irreducibles. The multiplicative monoid of monic
polynomials of Z_{p^n}[x] is a direct sum of monoids corresponding to
irreducible polynomials in Z_p[x], and we show that each of these monoids has
infinite elasticity. Moreover, for every positive integer m, there exists in
each of these monoids a product of 2 irreducibles that can also be represented
as a product of m irreducibles.
