> [!NOTE] Definition (Degree of a univariate polynomial forms) > Let $f\in R[x]$ be a non-zero [[Ring of Polynomial Forms|polynomial]] over $R$ in $x.$ The degree of $f,$ denoted $\deg(f),$ is the largest $k\in \mathbb{N}$ such that the coefficient of $x^{k}$ is non-zero. In this case the coefficient of $x^{k}$ is known as the **leading coefficient** of $f.$ > >The degree of the [[Zero Polynomial|zero polynomial]] is defined by $\deg(0)=-\infty.$ > [!NOTE] Definition (Degree of polynomial) > Contents # Properties See [[Degree of Product of Polynomials]]. By [[Degree of Product of Polynomials Over Integral Domain]], for $f,g\in D[x],$ $\deg(fg)=\deg(f)+\deg(g)$ where $D$ is an integral domain. Note that the [[Units of Ring of Polynomial Forms over Integral Domain|units of the ring of polynomial forms over a field]] are those with degree zero (constant polynomials).