Let be the real polynomial function, Prove that if for all such that then
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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
$$|a| + |b| + |c| + |d| \leq 7.$$
Source: Međunarodna matematička olimpijada, shortlist 1996
Školjka 
be the real polynomial function, 
Prove that if 
for all 
such that 
then 