In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalized version...

computed using the polynomial long division. If F is a field and f and g are polynomials in F[x] with g ≠ 0, then there exist unique polynomials q and r in F[x]...

systems get a short check value attached, based on the remainder of a polynomial division of their contents. On retrieval, the calculation is repeated and...

multiplication and division Elementary arithmetic Fourier division Polynomial long division Short division Weisstein, Eric W. "Long Division". MathWorld. "Islamic...

the polynomial remainder theorem or little Bézout's theorem (named after Étienne Bézout) is an application of Euclidean division of polynomials. It states...

synthetic division is a method for manually performing Euclidean division of polynomials, with less writing and fewer calculations than long division. It is...

concavity changes. Polynomial Coefficient Monomial Polynomial long division Synthetic division Polynomial factorization Rational function Partial fraction...

Euclidean division of polynomials, and, for hand-written computation, polynomial long division or synthetic division. One can define a division operation for...

0 1 ( x 6 − 4 x 5 + 5 x 4 − 4 x 2 + 4 − 4 1 + x 2 ) d x  using polynomial long division = ( x 7 7 − 2 x 6 3 + x 5 − 4 x 3 3 + 4 x − 4 arctan ⁡ x ) | 0...

_{t}.} As with polynomials of variables, a polynomial in the lag operator can be divided by another one using polynomial long division. In general dividing...

mathematics and computer algebra, factorization of polynomials or polynomial factorization expresses a polynomial with coefficients in a given field or in the...

the polynomial g ( x ) = f ( x ) ( x − a ) {\textstyle g(x)={\dfrac {f(x)}{(x-a)}}} , for example using polynomial long division or synthetic division. Conclude...

polynomials over a field the polynomial GCD may be computed, like for the integer GCD, by the Euclidean algorithm using long division. The polynomial...

quotient (integer division). In algebra of polynomials, the remainder is the polynomial "left over" after dividing one polynomial by another. The modulo...

especially in the field of algebra, a polynomial ring or polynomial algebra is a ring formed from the set of polynomials in one or more indeterminates (traditionally...

irreducible polynomial of degree n over GF(p), for instance using polynomial long division. Addition is the usual addition of polynomials, but the coefficients...

computer science, Horner's method (or Horner's scheme) is an algorithm for polynomial evaluation. Although named after William George Horner, this method is...

+ 2) is a polynomial factorization of x2 − 4. Factorization is not usually considered meaningful within number systems possessing division, such as the...

and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several...

be derived using geometric series as before, or by performing polynomial long division of 1 by ( x − 1 ) ( x − 2 i ) {\displaystyle (x-1)(x-2i)} , not...

considering polynomials, the order of the terms does not matter in general, as the addition is commutative. However, some algorithms, such as polynomial long division...

characterized by specification of a generator polynomial, which is used as the divisor in a polynomial long division over a finite field, taking the input data...

divided by f(X) in Ki[X]. The remainder r(X) can be computed through polynomial long division; however there is also a straightforward reduction rule that can...

arithmetic Chunking (division) Division algorithm Elementary arithmetic Fourier division Long division Polynomial long division Synthetic division G.P Quackenbos...

The Chebyshev polynomials are two sequences of orthogonal polynomials related to the cosine and sine functions, notated as T n ( x ) {\displaystyle T_{n}(x)}...

is found, a linear polynomial (x – r) can be factored out of the polynomial using polynomial long division, resulting in a polynomial of lower degree whose...

the discrete logarithm problem Polynomial long division: an algorithm for dividing a polynomial by another polynomial of the same or lower degree Risch...

roots are the roots of the other factor, which can be found by polynomial long division. This other factor is a q x 2 + b q + a p q 2 x + c q 2 + b p q...

originally restricted to integers, Euclidean division and the division theorem can be generalized to univariate polynomials over a field and to Euclidean domains...

Finding the roots of polynomials is a long-standing problem that has been extensively studied throughout the history and substantially influenced the...