Like all common terms in mathematics, "polynomial" has very slightly different definitions depending upon your reference text; but they differ only in superfluous ways.
Are there any canonical/popular definitions polynomial which allow them to have degree less than 1?
For example, is $\frac{1}{x} = x^{-1}$ a polynomial on $x$?
What about non-integer degrees? Is $\sqrt{x} = x^{0.5}$ a polynomial on $x$?