Question 16
(GDR 1) Let $F(n)$ be the set of polynomials $P(x)=a_0+a_1x+\cdots+a_nx^n$, with $a_0,a_1,\ldots,a_n\in\mathbb R$ and $0\le a_0=a_n\le a_1=a_{n-1}\le\cdots\le a_{[n/2]}=a_{[(n+1)/2]}$. Prove that if $f\in F(m)$ and $g\in F(n)$, then $fg\in F(m+n)$.