polynomials - 2024 PLAYTIME

Question

Newton’s identities give rearrangement formulae for the elementary symmetric variety of these functions. For 10 points each:

[10e] Name these functions expressed as sums of powers of a variable. Examples of these functions of degree 2 may be solved with the quadratic formula.

ANSWER: polynomials

[10m] By Gauss’s lemma, a primitive polynomial is irreducible over the integers if and only if it is irreducible over these numbers. A namesake theorem constrains roots in this set in terms of a polynomial’s first and last coefficients.

ANSWER: rational numbers [or rationals; accept Q]

[10h] Another sufficient criterion for the irreducibility of polynomials over the rational numbers is given by this German mathematician. Gauss apocryphally rated this mathematician on par with Newton and Archimedes.

ANSWER: Gotthold Eisenstein [or Ferdinand Gotthold Max Eisenstein]

<JC, Other Science - Math>

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Summary


2025 PLAYTIME @ CWRU	12/10/2024	Y	1	20.00	100%	100%	0%
2025 PLAYTIME @ Claremont	12/10/2024	Y	1	10.00	100%	0%	0%
2025 PLAYTIME @ Florida	12/10/2024	Y	3	13.33	100%	33%	0%
2024 PLAYTIME @ Harvard	04/26/2025	Y	4	17.50	100%	50%	25%
2024 PLAYTIME @ JHU	10/26/2024	Y	5	14.00	100%	20%	20%
2024 PLAYTIME @ JHU	10/26/2024	Y	1	20.00	100%	100%	0%
2025 PLAYTIME @ Northwest	12/10/2024	Y	4	12.50	75%	50%	0%
2025 PLAYTIME @ Sheffield	12/10/2024	Y	7	17.14	100%	57%	14%
2024 PLAYTIME @ UBC	10/05/2024	Y	1	20.00	100%	100%	0%
2024 PLAYTIME @ Virginia Tech	07/11/2025	Y	3	16.67	100%	33%	33%
2024 PLAYTIME @ WashU	10/12/2024	Y	6	18.33	100%	67%	17%

Data


Pittsburgh	Michigan A	10	10	0	20
girl 15 whale i mean they	Art of Premature Signaling	10	0	0	10
Edwin Laundrorat's Long-Lost Man Unclothès Rat Degrosses	Billy's Bastion	10	0	0	10
Too much from you lately	Keeping Up With the Cardassians	10	10	0	20
Project2025BC: Make Assyria Great Again	Qin Shi Huang's Immortality Poison	10	0	0	10
Brown	Belmont	10	10	10	30
BU	Brandeis	10	10	0	20
MIT	Harvard	10	0	0	10
Lexington	RIT	10	0	0	10
Catholic University of America	Haverford A	10	0	0	10
George Mason A	George Mason B	10	0	0	10
Maryland B	George Washington	10	0	0	10
Haverford B	CWRU	10	10	10	30
Georgetown	NYU A	10	0	0	10
Rutgers	Maryland A	10	10	0	20
Arizona State University A	UW A	10	10	0	20
South Dakota School of Mines	Carleton	10	0	0	10
UW B	Alberta	10	10	0	20
Washington Connections	Arizona State University B	0	0	0	0
Manchester	Cambridge	10	10	0	20
Birmingham	LSE	10	10	0	20
Warwick A	Sheffield A	10	10	10	30
Sheffield B	Imperial A	10	10	0	20
Edinburgh	Sheffield C	10	0	0	10
Lancaster	Warwick B	10	0	0	10
Warwick C	Imperial B	10	0	0	10
Waterloo A	Toronto B	10	10	0	20
Ashurbanipal’s Drag Race	Adrianne Lenker 4 Nobel Lit Prize 2K65	10	0	0	10
Even in Blacksburg There I Am	Master and Margaritaville	10	0	10	20
4 quizbowl pros go Virginia on North Carolina	Somehow Paula Deen Returned	10	10	0	20
Missouri	Chicago A	10	0	0	10
SIUE	Illinois B	10	0	0	10
WashU Squirtle	Illinois C	10	10	0	20
Iowa State	WashU Bulbasaur	10	10	0	20
Illinois A	Truman State	10	10	10	30
Chicago B	WashU Charmander	10	10	0	20