A problem in polynomials to show there are polynomials $f_{1}(x), \cdots f_{k}(x)$ such that $ P(x) = \sum_{j = 1}^{k} (f_{j} (x))^{2}$

Question

Let $P(x) \in \mathbb{R}$ be non negative $\forall x \in \mathbb{R}$. Prove That, for some $k$, there are polynomials $f_{1}(x), \cdots f_{k}(x)$ such that $$ P(x) = \sum_{j = 1}^{k} (f_{j} (x))^{2}$$

This problem is a classical polynomial problem. Now I have not found any clue to solving it. I have some plans of applying Vietas theorem to it.. But it failed. I need some help to start off. A little bit wordy and rigorous proof is appreciable.