IMO 1996 - Shortlisted problems Question 5

A5 (ROM) Let $P(x)$ be the real polynomial function $P(x)=ax^3+bx^2+cx+d$. Prove that if $|P(x)|\le1$ for all $x$ such that $|x|\le1$, then
$$|a|+|b|+|c|+|d|\le7.$$