I'm trying to proof that the Curve $C:xz^3-y^4+2y^2z^2-z^4=0$ is irreducible for all fields K, with $char(K)>2$. I know that the point $(1:0:0)$ is the only singular point and its multiplicity is 3. How can I argument that this curve is irreducible? I guess that I may use Bezeout's Theorem, but I'm not able to write a good argumentation.
2026-03-27 20:30:47.1774643447
Quartic with only one singular point
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