100 English words for '(of a polynomial) Given a polynomial p over a field K, the smallest extension field L of K such that p, as a polynomial over L, decomposes into linear factors (polynomials of degree 1); (of a set of polynomials) given a set P of polynomials over K, the smallest extension field of K over which every polynomial in P decomposes into linear factors.'

splitting field

normal extension

Gauss-Lucas theorem

monic

separable extension

conjugate

normal

quartic function

quintic function

Ax-Grothendieck theorem

Euler's criterion

separable polynomial

minimal polynomial

Jacobi polynomial

algebraic

algebraic extension

algebraically closed

eigencurve

Herbrand-Ribet theorem

primitive polynomial

algebraically independent

elliptic curve

multinomial

Löb's theorem

polynome

polynomic

irreducible

Ax-Kochen theorem

polynomial

polynomially

polynomialist

transcendence degree

central simple algebra

p-adic absolute value

vanishing ideal

algebraic number

Tarski-Seidenberg theorem

parallel postulate

p-adic ordinal

Durand-Kerner method

projective variety

p-adic norm

Abel polynomial

polynomial basis

Appell sequence

P-complete

quadratic reciprocity

Legendre symbol

Diophantine equation

Sturm sequence

perfect field

Zeisel number

all-one polynomial

Schinzel's hypothesis H

Frobenius endomorphism

nonic

Sheffer sequence

Horner's rule

Tschirnhaus transformation

prodiscrete

p-adic number

p-adic ultrametric

algebraic closure

semisimple

fewnomial

Fermat's little theorem

rational root theorem

Hermite polynomial

Sturm's theorem

Voronoi formula

Gröbner basis

rational function

simple root

decidable

bidegree

quantic

Richardson's theorem

nonpolynomial

characteristic polynomial

cissoid

anticyclotomic

epimorphism

presemifield

Jacobian conjecture

softplus

Witt group

invex

quadratic function

Morse function

compact

biquadratic