Euclidean Division
Polynomial division allows to prove that for every pair polynomials (A, B) such that B is not the zero polynomial, there exists a quotient Q and a remainder R such that
and either R=0 or degree(R) < degree(B). Moreover (Q, R) is the unique pair of polynomials having this property. written in a divisor–quotient form which is often advantageous. Consider polynomials P(x), D(x) where degree(D) < degree(P). Then, for some quotient polynomial Q(x) and remainder polynomial R(x) with degree(R) < degree(D),
This existence and unicity property is known as Euclidean division and sometimes as division transformation.
Read more about this topic: Polynomial Long Division
Famous quotes containing the word division:
“The glory of the farmer is that, in the division of labors, it is his part to create. All trade rests at last on his primitive activity.”
—Ralph Waldo Emerson (1803–1882)