Question

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 varieties. Hilbert’s basis theorem applies to rings of these objects, which are formed by adjoining (10[1])dummy variables to rings like the complex numbers. Gauss’s lemma concerns the irreducibility of these objects, whose solvability can be determined via their (10[1])Galois (“gal-WAH”) groups. (10[1])Vieta’s formulas provide explicit relations between (10[1])solutions to these objects, which have no generic solution in degree five or higher by the Abel–Ruffini theorem. For 10 points, the fundamental theorem of algebra concerns the roots of what functions? ■END■ (10[1])

ANSWER: polynomials [accept monomials; accept polynomial rings or polynomial equations]
<UNC A, Other Science>
= Average correct buzz position

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Buzzes

PlayerTeamOpponentBuzz PositionValue
Stan MelkumianPurdueStanford B5710
Stephen WalshNorthwestern BNotre Dame A8010
Sharath NarayanNorthwestern AIowa8210
Jonah HubertNotre Dame BNotre Dame C8810
Rachel EzrielevGeorgetown AGeorgetown B12110

Summary

California2025-02-01Y3100%0%0%58.33
Florida2025-02-01Y3100%0%0%97.33
Great Lakes2025-02-01Y6100%0%17%89.83
Lower Mid-Atlantic2025-02-01Y6100%0%17%96.00
Midwest2025-02-01Y6100%0%0%70.83
North2025-02-01Y3100%0%0%60.67
Northeast2025-02-01Y5100%0%20%59.00
Overflow2025-02-01Y5100%0%0%85.60
South Central2025-02-01Y2100%0%0%78.50
Southeast2025-02-01Y3100%0%0%46.33
UK2025-02-01Y10100%0%0%68.20
Upper Mid-Atlantic2025-02-01Y786%0%14%77.67
Upstate NY2025-02-01Y3100%0%0%69.67