Find (with proof) all monic polynomials f(x) with integer coefficients that satisfy the following two conditions.
1- f(0)=2004.
2- If x is irrational, then f(x) is also irrational.
(Notes: A polynomial is monic if its highest degree term has coefficient 1. Thus, f(x)=x^{4}-5 x^{3}-4 x+7 is an example of a monic polynomial with integer coefficients.
A number x is rational if it can be written as a fraction of two integers. A number x is irrational if it is a real number which cannot be written as a fraction of two integers. For example, 2/5 and -9 are rational, while \sqrt{2} and \pi are well known to be irrational.)