(algebra, field theory) A polynomial over a given field that has distinct roots in the algebraic closure of said field (the number of roots being equal to the degree of the polynomial).

(algebra) polynomial ring

(mathematics) Any member of a polynomial sequence which can be considered as a generalization of the Fibonacci numbers.

(mathematics) For a given set of points (x_j,y_j) with no two x_j values equal, the polynomial of lowest degree that assumes at each value x_j the corresponding value y_j, so that the functions coincide at each point.

(combinatorics) A generating polynomial of the number of ways to place non-attacking rooks on a generalized form of chessboard.

(mathematics) Any member of a classical orthogonal polynomial sequence having diverse applications.

(mathematics) Any member of a certain polynomial sequence Dₙ(x,α).

(mathematics) Any member of a polynomial sequence of binomial type defined by T_n(x)=∑ₖ₌₀ⁿS(n,k)xᵏ=∑ₖ₌₀ⁿn atop kxᵏ, where S(n,k)=n atop kis a Stirling number of the second kind, i.e. the number of partitions of a set of size n into k disjoint non-empty subsets.

(combinatorics) Any member of a certain class of polynomials used in the study of set partitions, and related to Stirling numbers and Bell numbers.

(mathematics) Any member of a certain class of orthogonal polynomials.