Question

Is anybody familiar with Extended Eisenstein Theorem? I need to prove a variation of the statement, as follows:
Let \(f(x)=a_0+a_1x^1+a_2x^2+\cdots+a_nx^n\) where \(a_i\) are integers. Let \(q\) be a prime such that \(q \mid a_0, a_1, \dots, a_{n-1}, q\nmid a_n, q^2 \nmid a_0\). Prove that f(x) cannot be factored into polynomials with integer coefficients.