AUSTRIAN-POLISH 1995 Problem 3

Let $P(x) = x^4 + x^3 + x^2 + x + 1$ . Show that there exist two non-constant polynomials $Q(y)$ and $R(y)$ with integer coefficients such that for all $Q(y) \cdot R(y)= P(5y^2)$ for all $y$ .