The highest order power in a univariate polynomial is known as its order (or, more properly, its polynomial degree). For example, the polynomial P(x) = a_n x^n + ... + a_2 x^2 + a_1 x + a_0 is of order n, denoted deg P(x) = n. The order of a polynomial is implemented in the Wolfram Language as Exponent[poly, x]. It is preferable to use the word "degree" for the highest exponent in a polynomial, since a completely different meaning is given to the word "order" in polynomials taken modulo some integer (where this meaning is the one used in the multiplicative order of a modulus). In particular, the order of a polynomial P(x) with P(0)!=0 is the smallest integer e for which P(x) divides x^e + 1.

irreducible polynomial | multiplicative order | polynomial degree | primitive polynomial