A function of this type can approximate any other continuous function as closely as wanted by the Stone-Weierstrass Theorem, and according to Abel's Impossibility Theorem, formulas for solving those above a certain (*) degree do not exist.
The Hilbert Basis Theorem concerns rings of these constructs. A function of this type can approximate any other continuous function as closely as wanted by the Stone-Weierstrass Theorem, and according to Abel's Impossibility Theorem, formulas for solving those above a certain (*) degree do not exist. Descartes' Rule of Signs can be used to determine the sign of their roots. By the Fundamental Theorem of Algebra, their total number of zeros is equal to the degree of their highest term. For 10 points, name this type of expression exemplified by monomials, as well as x squared plus x plus 1.
The Hilbert Basis Theorem concerns rings of these constructs.
 polynomials