Euclidean division
This differs from the Euclidean division of integers in that, for the integers, the degree condition is replaced by the bounds on the remainder "r" (non-negative and less than the divisor, which insures that "r" is unique.) The similarity between Euclidean division for integers and that for polynomials motivates the search for the most general algebraic setting in which Euclidean division is valid. The rings for which such a theorem exists are called Euclidean domains, but in this generality, uniqueness of the quotient and remainder is not guaranteed.