Zero polynomial 
Possible Duplicate:
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?

Persistance.
You want formulas to make sense also when abusively applying them to cases involving the zero polynomial.
For example, we have $\deg(f\cdot g)=\deg f +\deg g$ and $\deg (f+g)\le \max\{\deg f, \deg g\}$. Therefore we assign a symbolic value - and be it only for mnemonic purposes - of $-\infty$ as the degree of $0$, because that makes $-\infty =\deg(0\cdot g)=-\infty+\deg g$ and $\deg g = \deg (0+g)=\max\{-\infty,\deg g\}$ work.
