Binomial (polynomial): Difference between revisions

→‎Definition: m and n do not need to both be negative in order to form a Laurent binomial
(→‎Definition: If, "in some contexts, the exponents m and n may be negative", then we should not say they must be non-negative)
(→‎Definition: m and n do not need to both be negative in order to form a Laurent binomial)
A binomial is a polynomial which is the sum of two [[monomial]]s. A binomial in a single indeterminate (also known as a [[univariate]] binomial) can be written in the form
:<math>a x^n - bx^m \,,</math>
where <math>a</math> and <math>b</math> are [[number]]s, and <math>n</math> and <math> m</math> are distinct [[integer]]s and <math>x</math> is a symbol which is called an [[indeterminate (variable)|indeterminate]] or, for historical reasons, a [[variable (mathematics)|variable]]. In some contexts, the exponents <math>m</math> andor <math>n</math> (or both) may be negative, in which case the expression is a [[Laurent polynomial|Laurent binomial]].
 
More generally, a binomial may be written<ref name=Sturmfels62>{{Cite journal