Binomial (polynomial): Difference between revisions

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==Definition==
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^nm - bx^mn \,,</math>
where <{{math>|''a</math>''}} and <{{math>|''b</math>''}} are [[number]]s, and <{{math>n</math>|''m''}} and <{{math> m</math>|''n''}} 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 the context of [[Laurent polynomial]]s, a ''Laurent binomial'', often simply called ''binomial'' is similarly defined, but the exponents <math>m</math> and <math>n</math> may be negative.
 
More generally, a binomial may be written<ref name=Sturmfels62>{{Cite journal