Polynomial of degree 2/K/Expanded/Definition

A quadratic polynomial ${\displaystyle {}F\in K[X_{1},\ldots ,X_{n}]}$ over a field ${\displaystyle {}K}$ is a polynomial of degree ${\displaystyle {}2}$; that is, an expression of the form

${\displaystyle {}F=\sum _{i\leq j}a_{ij}X_{i}X_{j}+\sum _{i=1}^{n}b_{i}X_{i}+c\,,}$

where ${\displaystyle {}a_{ij},b_{i},c\in K}$.