Question

One of these objects provides the weight in Gauss–Jacobi quadrature. Sergei Bernstein names a type of these objects that are used to construct a more general class of objects around control points. Before it was generalized by Stone, these objects were doing the "approximation" in the Weierstrass ("VYE-er-stross") approximation theorem. Namesake simple "nodes" characterize examples of these objects named for (*) Chebyshev, which can (0[1])mitigate Runge's ("ROON-guh's") phenomenon. Barycentric weights define a type of these objects that were used by Lagrange for interpolation. These objects are partial sums of Taylor series. The fundamental theorem of algebra describes the roots of these (10[1])expressions. (10[1])For 10 points, name these sums of monomials. ■END■ (10[1])

ANSWER: polynomials [accept cyclotomic polynomials or Bernstein polynomials or Chebyshev polynomials or Chebyshev polynomials of the first kind or Chebyshev polynomials of the second kind] (Bernstein polynomials are used to construct Bézier curves.)
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TournamentEditionExact Match?TUHConv. %Power %Neg %Average Buzz
2025 PACE NSC06/07/2025Y3100%0%0%100.67