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I know a homogeneous polynomial $f(x,y)$ is irreducible if and only if $f(x,1)$ is. (Proof?)

I'm wondering if there's a similar criterion to check if $f(x,y)+c$ is irreducible, given that $f$ is homogeneous and irreducible.

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    What do you mean by irreducible here? How could any monomial with total degree greater than 1 be irreducible? $xy^2$ seems like a counterexample, at my current (low) level of understanding.2012-09-06

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