Is 0 (zero) considered a polynomial?
It absolutely is a polynomial. If it weren’t, we wouldn’t have polynomial rings (an essential structure in abstract algebra) as the zero polynomial plays the role of the additive identity. Although constant polynomials are generally considered to have degree zero, I’ve seen the zero polynomial defined to have degree -1. I don’t know how common this definition is, but if I remember correctly, it’s done for the sake of consistency with certain theorems involving the degree of polynomials. @Packer Fan: Sets of polynomials under addition and multiplication do not form a field, as there is generally a lack of multiplicative inverses. They do, however, form a ring if we choose coefficients from a ring. Even better, if we choose coefficients from an integral domain, the polynomial ring will be an integral domain as well.
