# Bounds on coefficients of factors of a multivariate polynomial

If I have a multivariate polynomial $F(x, y, ..)$ what is the smallest bound B that I can quickly find such that $|G|_{\infty} \le B$ for all factors $G$ of $F$. (I'm using $|G|_{\infty}$ to denote the largest coefficient in G.)

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A bound in terms of what quantity? Is it the largest coefficient of $F$, or something else? –  user53153 Feb 8 '13 at 20:05