Binomial (polynomial): Difference between revisions

→‎Definition: If, "in some contexts, the exponents m and n may be negative", then we should not say they must be non-negative
(→‎Definition: There ought to be some example in which a and b are not integers and in which the exponent has a higher power than 2, in order to show that this is possible)
(→‎Definition: If, "in some contexts, the exponents m and n may be negative", then we should not say they must be non-negative)
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 [[nonnegative 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> and <math>n</math> 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