parmenides51 wrote: Prove that for any polynomial $f(x)$ (with real coefficients) there exist polynomials $g(x)$ and $h(x)$ (with real coefficients) such that $f(x) = g(h(x)) - h(g(x))$. It is easy and classical to show that any polynomial $P(x)$ may be written as $Q(x+1)-Q(x)$ for some polynomial $Q(x)$ Write then $f(x)+1=g(x+1)-g(x)$, which is $f(x)=g(x+1)-(g(x)+1)$ $=g(h(x))-h(g(x))$ with $h(x)=x+1$