RU-ALLRUSSIAN 1973 Problem 5

$\mathrm{p}(\mathrm{x}) = \mathrm{ax}^2 +\mathrm{bx} + \mathrm{c}$ is a real quadratic such that $\mathrm{lp}(\mathrm{x})\leq 1$ for all $|\mathrm{x}|\leq 1$ . Prove that $|\mathrm{cx}^2 +\mathrm{bx} + \mathrm{al}\leq 2$ for $|\mathrm{x}|\leq 1$ .