In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalised version of the familiar arithmetic technique called long division. It can be done easily by hand, because it separates an otherwise complex division problem into smaller ones.
Polynomial long division is an algorithm that implement the Euclidean division of polynomials, which starting from two polynomials A (the dividend) and B (the divisor) produces, if B is not zero, a quotient Q and a remainder R such that
- A = BQ + R,
and either R = 0 or the degree of R is lower than the degree of B. These conditions define uniquely Q and R, which means that Q and R do not depend on the method used to compute them.
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