The highest power in a univariate polynomial is known as its degree, or sometimes "order." For example, the polynomial P(x) = a_n x^n + ... + a_2 x^2 + a_1 x + a_0 is of degree n, denoted deg P(x) = n. The (structural) degree of a polynomial is implemented in the Wolfram Language as Exponent[poly, x]. Richardson's theorem proves that it is recursively undecidable to determine the degree of an arbitrary polynomial.

degree | polynomial | polynomial order | Richardson's theorem