IN-TST 2009 Problem 5

Let $f(x)$ and $g(y)$ be two monic polynomials of degree= $n$ having complex coefficients. We know that there exist complex numbers $a_i,b_i,c_i \forall 1\le i \le n$ , such that $f(x)-g(y)=\prod_{i=1}^n{(a_ix+b_iy+c_i)}$ . Prove that there exists $a,b,c\in\mathbb{C}$ such that $f(x)=(x+a)^n+c\text{ and }g(y)=(y+b)^n+c$ .