Editing Polynomial long division (section)

== Euclidean division ==
{{anchor|Division transformation}}
{{main|Euclidean division of polynomials}}
For every pair of polynomials (''A'', ''B'') such that ''B'' ≠ 0, polynomial division provides a ''quotient'' ''Q'' and a ''remainder'' ''R'' such that 
:<math>A=BQ+R,</math>
and either ''R''=0 or degree(''R'') < degree(''B''). Moreover (''Q'', ''R'') is the unique pair of polynomials having this property.

The process of getting the uniquely defined polynomials ''Q'' and ''R'' from ''A'' and ''B'' is called ''Euclidean division'' (sometimes ''division transformation''). Polynomial long division is thus an [[algorithm]] for Euclidean division.<ref>{{cite book|author=S. Barnard|title=Higher Algebra|year=2008|publisher=READ BOOKS|isbn=978-1-4437-3086-0|page=24}}</ref>