Degree of polynomial, deg p

A polynomial $p \in \mathcal P(\mathbf F)$ is said to have degree $m$ if there exist scalars $a_0,a_1,\dots,a_m \in \mathbf F$ with $a_m \ne 0$ such that

for all $z \in \mathbf F$. If $p$ has degree $m$, we write $\deg p = m$.

The polynomial that is identically $0$ is said to have degree $-\infty$.