Let $P\in {\mathbb Z}[X]$ be a polynomial,
$$ P=\sum_{k=0}^{n} a_kx^k $$ Let us put $$ || P || = \max_{0 \leq k \leq n} |a_k| $$
Let $Q$ be a factor of $P$. Can we bound $||Q||$ by some function of $||P||$ ? If so, is an asymptotically optimal bound known ?