TITLE: Why is the zero polynomial not assigned a degree?
QUESTION [14 upvotes]: Yesterday, I read in my textbook,

We assign degree to every polynomial and even a non-zero constant is assigned a degree $0$ but $0$ itself is not assigned a degree.

Why is that? Why we don't assign degree $0$ to the zero polynomial?

REPLY [2 votes]: The degree of a polynomial is the exponent of the term with the highest power (and non-zero coefficient).
$$5x-4x^4+2\to x^4\to 4$$
$$0x^{45}+1x^3+2x^2\to x^3\to3$$
$$21\to x^0\to0$$
$$0\to ??$$
The null polynomial contains no power of the variable.