Hilbert's basis theorem states that certain rings of these objects are Noetherian, and Eisenstein's criterion tests for their irreducibility over the rationals.
Hilbert's basis theorem states that certain rings of these objects are Noetherian, and Eisenstein's criterion tests for their irreducibility over the rationals. The Abel-Ruffini theorem states the impossibility of a solution in radicals for some of these expressions. Descartes' Rule of Signs can be used to find the number of positive, negative, and complex solutions to one of these, and the Fundamental Theorem of Algebra states that they have a number of roots equal to their degree. They are infinitely differentiable and cross the x-axis at their roots. For 10 points, name these expressions composed of variables and their powers, written as sums of monomials.
Hilbert's basis theorem states that certain rings of these objects are Noetherian, and Eisenstein's criterion tests for their irreducibility over the rationals.
polynomials 