An ordering of terms within these mathematical objects is denoted by the shorthand “grevlex.” A set of these objects is iteratively transformed by Büchberger’s algorithm to obtain a Gröbner basis. Solution sets to systems of equations defined by these objects are called algebraic (10[1])varieties. Hilbert’s basis theorem applies to rings of these objects, which are formed by adjoining dummy variables to rings like the complex numbers. Gauss’s lemma concerns the irreducibility of these objects, whose solvability can be determined via their Galois (“gal-WAH”) groups. (10[1])Vieta’s formulas provide explicit relations (-5[1])between solutions to these objects, which have no generic solution in degree five or higher by the Abel–Ruffini (10[2])theorem. For 10 points, the fundamental theorem of algebra concerns the roots of what functions? ■END■ (10[2])