The degree of the zero polynomial is usually taken to be “undefined.” In more detail:

  • A polynomial’s degree is the highest power of xxx that has a non-zero coefficient.
  • The zero polynomial is 000 (or 0x+0x2+…0x+0x^2+\dots 0x+0x2+…), where all coefficients are zero.
  • Since it has no non-zero term at all , there is no power of xxx to look at, so we cannot assign a usual degree.
  • That’s why, in most school-level maths, the correct statement is:

The degree of the zero polynomial is not defined (or undefined).

In more advanced contexts, some mathematicians choose to define its degree as −1-1−1 or −∞-\infty −∞ to make certain algebraic theorems (like degree of a product or sum) work smoothly, but for exams and standard textbooks, the safe and accepted answer is:

✅ Degree of the zero polynomial: undefined / not defined.