Affine Hyperquadrics

Let \(n\geq 1\) be a fixed natural number. For every integer \(d\geq 1\) , each polynomial \(F(X_1,\dotsc ,X_n) \in K[X_1,\dotsc , X_n]_d\) is represented as \(\displaystyle F=F_d+F_{d-1}+\cdots +F_1+F_0, \) where \(F_i\) is a homogeneous polynomial of degree i, \(i=1,2,\ldots ,d\) , \(F_0\in K\) and \(F_d\neq 0\) .