ISL 1979 Problem 38

Prove the following statement: If a polynomial $f(x)$ with real coefficients takes only nonnegative values, then there exists a positive integer $n$ and polynomials $g_1(x), g_2(x),\cdots, g_n(x)$ such that $$f(x) = g_1(x)^2 + g_2(x)^2 +\cdots+ g_n(x)^2$$