Degree of a polynomial

Remarks

The degree of $3x^4 - x + 2$ in $\mathbb{Z}[x]$ is $4$. A nonzero constant polynomial has degree $0$. Some authors leave $\deg 0$ undefined, or set it to $-1$. The convention $-\infty$ makes the formula $\deg(f g) = \deg f + \deg g$ hold also for $f = 0$ or $g = 0$. For all $f, g \in R[x]$, $\deg(f + g) \le \max(\deg f, \deg g)$. The coefficient $a_d$ with $d = \deg f$ is the leading coefficient of $f$.