An ordering of terms within these mathematical objects is denoted by the shorthand “grevlex.” (10[1])A set of these objects is iteratively transformed by Büchberger’s algorithm to obtain a Gröbner basis. (10[3])Solution sets to systems (10[2])of equations (10[2])defined by these objects are (10[1])called algebraic (10[1])varieties. Hilbert’s (10[1])basis theorem (10[3])applies to rings (10[1])of these objects, (10[3])which are formed by adjoining (10[1])dummy (10[1])variables to rings (10[1])like the complex numbers. (10[1])Gauss’s lemma concerns the irreducibility of these objects, (10[3])whose solvability (10[1])can be (10[1])determined (-5[1])via their (10[1])Galois (10[1])(“gal-WAH”) groups. (10[8])Vieta’s (10[1])formulas provide (10[1])explicit relations (10[1]-5[1])between (10[1])solutions (-5[1])to these objects, (10[5])which have (10[1])no generic (10[2])solution in degree five or higher (10[2]-5[1])by (10[1])the Abel–Ruffini (10[2])theorem. (10[1])For 10 points, the fundamental theorem of algebra (10[1])concerns the roots of what functions? ■END■ (10[5]0[1])