High Quality Content by WIKIPEDIA articles! In mathematics, the Cayley–Bacharach theorem is a statement about cubic curves (plane curves of degree three) in the projective plane mathbb{P}^2. The original form states: Assume that two cubics C1 and C2 in the projective plane meet in nine (different) points, as they do in general. Then every cubic that passes through any eight of the points also passes through the ninth point.

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