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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 of and a polynomial in of degree one less than the degree of .
The rings for which such a theorem exists are called Euclidean domains, but in this generality, uniqueness of the quotient and remainder is not guaranteed. [ 8 ] Polynomial division leads to a result known as the polynomial remainder theorem : If a polynomial f ( x ) is divided by x − k , the remainder is the constant r = f ( k ).
Remainder theorem may refer to: Polynomial remainder theorem; Chinese remainder theorem This page was last edited on 29 December 2019, at 22:03 (UTC). Text is ...
CRT – Chinese remainder theorem. csc – cosecant function. (Also written as cosec.) csch – hyperbolic cosecant function. (Also written as cosech.) ctg – cotangent function. (Also written as cot.) curl – curl of a vector field. (Also written as rot.) cvc – covercosine function. (Also written as covercos.) cvs – coversine function.
The quotient and remainder may be computed by any of several algorithms, including polynomial long division and synthetic division. [19] When the denominator b(x) is monic and linear, that is, b(x) = x − c for some constant c, then the polynomial remainder theorem asserts that the remainder of the division of a(x) by b(x) is the evaluation a ...
Mountain pass theorem (calculus of variations) Moving equilibrium theorem ; Multinomial theorem (algebra, combinatorics) Multiplication theorem (special functions) Multiplicity-one theorem (group representations) Mumford vanishing theorem (algebraic geometry) Mutual fund separation theorem (financial mathematics)
Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011.
Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.
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