ISL 1996 A5

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

$|a| + |b| + |c| + |d| \leq 7.$

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