As is a homogeneous polynomial in two indeterminates, the fundamental theorem of algebra implies that is a product of linear polynomials. If one defines the multiplicity of a common zero of and as the number of occurrences of the corresponding factor in the product, Bézout's theorem is thus proved.
As is a homogeneous polynomial in two indeterminates, t.he fundamental theorem of algebra implies that is a product of linear polynomials If one defines the multiplicity of a common zero of and as the number of occurrences of the corresponding factor in the product, Bézout's theorem is thus proved.