It is shown that if f(x) is a polynomial in Z left bracket alpha right bracket left bracket x right bracket , where alpha satisfies a monic irreducible polynomial over Z, then f(x) can be factored over Q( alpha ) left bracket x right bracket in polynomial time. It is also shown that the splitting field of f(x) can be determined in time polynomial in ( left bracket Splitting field of f(x):Q right bracket ,log vertical f(x) vertical ).