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:
“For a small child there is no division between playing and learning; between the things he or she does “just for fun” and things that are “educational.” The child learns while living and any part of living that is enjoyable is also play.”
—Penelope Leach (20th century)