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Long division. In arithmetic, long division is a standard division algorithm suitable for dividing multi-digit Hindu-Arabic numerals (positional notation) that is simple enough to perform by hand. It breaks down a division problem into a series of easier steps. As in all division problems, one number, called the dividend, is divided by another ...
Polynomial long division is an algorithm that implements 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. and either R = 0 or the degree of R is lower than the degree of B. These conditions uniquely define Q and R ...
In abstract algebra, given a magma with binary operation ∗ (which could nominally be termed multiplication), left division of b by a (written a \ b) is typically defined as the solution x to the equation a ∗ x = b, if this exists and is unique. Similarly, right division of b by a (written b / a) is the solution y to the equation y ∗ a = b ...
Ruffini's rule. In mathematics, Ruffini's rule is a method for computation of the Euclidean division of a polynomial by a binomial of the form x – r. It was described by Paolo Ruffini in 1809. [1] The rule is a special case of synthetic division in which the divisor is a linear factor.
In algebra, the polynomial remainder theorem or little Bézout's theorem (named after Étienne Bézout) [1] is an application of Euclidean division of polynomials. It states that, for every number any polynomial is the sum of and the product by of a polynomial in of degree less than the degree of In particular, is the remainder of the Euclidean ...
Pre-calculus combines algebra, analytic geometry, and trigonometry. Topics in algebra include the binomial theorem, complex numbers, the Fundamental Theorem of Algebra, root extraction, polynomial long division, partial fraction decomposition, and matrix operations.