Zero polynomial 
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Polynomial of degree $-\infty$? 

Today in Abstract Algebra my instructor briefly mentioned that sometimes the zero polynomial is defined to have degree $-\infty$. What contexts have caused this to become convention?

We want $\deg(P\cdot Q)=\deg P+\deg Q$ for two polynomials. In particular $\deg\mathbf 0=\deg P+\deg\mathbf 0$, so we can't take an integer. $+\infty$ could be a choice as we want $\deg(P+Q)\leq \max(\deg P,\deg Q)$ but with the definition $\deg((\alpha_j)_{j\geq 0}:=\sup\{k\geq 0\mid \alpha\neq 0\}$, we take a supremum over an emptyset, so we take $-\infty$.
