Let $ f \in k[x,y]$ a polynomial. Then $ f$ can have more factors in the factorization over $ k[[x]][y]$ than over $ k[x,y]$ . Is it possible for $ f$ to have multiple factors in $ k[[x]][y]$ if it does not have multiple factors in $ k[x,y]$ ? It looks like an easy question but I cant find a simple argument.
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