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:
“Don’t order any black things. Rejoice in his memory; and be radiant: leave grief to the children. Wear violet and purple.... Be patient with the poor people who will snivel: they don’t know; and they think they will live for ever, which makes death a division instead of a bond.”
—George Bernard Shaw (1856–1950)