Bézout's theorem

Bézout's theorem states that, for two algebraic curves in the plane that do not share any common components, the maximum number of points where they intersect is equal to the product of their degrees. The degree of a curve measures its complexity—like how many times it might cross a line. For example, a line (degree 1) and a circle (degree 2) can intersect at most two points. This theorem provides a way to predict the number of intersection points based on the curves' degrees, counting intersections with multiplicity (including tangencies and overlaps).