factorisation of analytic functions

If I have an analytic function in plane $F(x,y)$ that is zero on a curve $y=f(x)$, is it true that $F=(y-f(x))^n h$, where $h$ is nonzero on the curve? More general, can be somethink said about factorisation of analytic functions? How much is it determined by its zero set? Thx

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You are using $f$ for two different things... –  Mariano Suárez-Alvarez Oct 14 '10 at 14:58
Thank you very much. Does somethink like that hold also over the reals? Peter –  peter franek Oct 14 '10 at 20:38
Yes it does.... –  Thierry Zell Oct 14 '10 at 20:45