For 10 points, name these functions which consist of a sum of coefficients times powers of a variable, such as "x-cubed plus two-x-squared minus one."
These entities can be used to arbitrarily closely approximate a continuous function on a closed interval according to the Stone-Weierstrass theorem. These functions intersect at knots in splines, which are constructed piecewise from them for purposes of interpolation. A method named for Cardano demonstrates how to find the solutions to one subclass of this family of functions, and Abel and Ruffini proved there was no general solution to them when their degree was greater than four. For 10 points, name these functions which consist of a sum of coefficients times powers of a variable, such as "x-cubed plus two-x-squared minus one."
These entities can be used to arbitrarily closely approximate a continuous function on a closed interval according to the Stone-Weierstrass theorem.
polynomials