Let
![P(x)](/media/m/c/d/7/cd7664875343d44cd5f96a566b582b0e.png)
be the real polynomial function,
![P(x) = ax^3 + bx^2 + cx + d.](/media/m/e/6/c/e6c9eee335cb463a987a60179f4a6456.png)
Prove that if
![|P(x)| \leq 1](/media/m/9/6/8/968399f54b34f1e0569d42583f5e1a91.png)
for all
![x](/media/m/f/1/8/f185adeed9bd346bc960bca0147d7aae.png)
such that
![|x| \leq 1,](/media/m/8/0/c/80cb8a707e54b918a5416e5ad058633e.png)
then
%V0
Let $P(x)$ be the real polynomial function, $P(x) = ax^3 + bx^2 + cx + d.$ Prove that if $|P(x)| \leq 1$ for all $x$ such that $|x| \leq 1,$ then
$$|a| + |b| + |c| + |d| \leq 7.$$