For 10 points, name these mathematical constructs composed of coefficient and associated variable terms.
The Horner scheme is a common computer-science exercise as a method for evaluating them, and the Legendre ones results from solving Laplace's equations in spherical coordinates. Chebyshev's fill an important role in interpolation theory and provide a method of writing trig identities solely in terms of the originating functions. Tartaglia and Cardano devised formulas for solving up to fourth degree ones, but Abel proved that fifth degree ones have no general algebraic solution. For 10 points, name these mathematical constructs composed of coefficient and associated variable terms.
The Horner scheme is a common computer-science exercise as a method for evaluating them, and the Legendre ones results from solving Laplace's equations in spherical coordinates.
{polynomial}