If http://latex.codecogs.com/png.latex?...thbb{Z}[x], then http://latex.codecogs.com/png.latex?f(x) factors into a product of two polynomials of lower degrees http://latex.codecogs.com/png.latex?...thbb{Q}[x] if and only if it has such a factorization with polynomials of the same degrees

http://latex.codecogs.com/png.latex?...thbb{Z}[x].

How to prove it??