SCHWEITZER 1963 Problem 4

Call a polynomial positive reducible if it can be written as a product of two nonconstant polynomials with positive real coefficients. Let $f(x)$ be a polynomial with $f(0)\not=0$ such that $f(x^n)$ is positive reducible for some natural number $n$ . Prove that $f(x)$ itself is positive reducible. [L. Redei]