Thedegreeof thezero polynomialis either left undefined, or is defined to be negative (usually −1 or ). Like any constant value, the value 0 can be considered as a (constant)polynomial, called thezero polynomial. It has no nonzero terms, and so, strictly speaking, it has nodegreeeither.

Well, it depends.

Mathematical practice shows that sometimes it is useful to define the degree of the zero polynomial to be zero, sometimes to define it to be−∞−∞and sometimes to leave is undefined. Which option one chooses depends on what one is trying to do.

This is quite different with what happens with the degree of all other polynomials, which is always defined in the same way (*) But don't think that if for the slightiest of reasons we were to fnd it useful to change the definition to do something we wanted, we would.

(*) Actually, that is not exactly true: we sometimes put degrees on polynomials which are different from the usual ones, but usually only on polynomials with more than one variable.