# Intersection of line and surface

A straight line in 3 space can be described as A + Bt, where A is a position, B a direction, and t a scalar parameter. CAD surfaces can be represented in terms of polynomial functions of two variables (u and v) with the highest degree term being $u^nv^n$. The intersections can then be obtained as roots of a polynomial in t. I have seen proofs that for n = 2 or n = 3, the polynomial in t is of 8th or 18th degree respectively $(2n^2)$.

Question: Does this relationship $(2n^2)$ hold for n > 3?