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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). [9] [10]
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 ...
Thus, the function may be more "cheaply" evaluated using synthetic division and the polynomial remainder theorem. The factor theorem is another application of the remainder theorem: if the remainder is zero, then the linear divisor is a factor. Repeated application of the factor theorem may be used to factorize the polynomial. [3]
Chevalley–Warning theorem (field theory) Chinese remainder theorem (number theory) Choi's theorem on completely positive maps (operator theory) Chomsky–Schützenberger enumeration theorem (formal language theory) Chomsky–Schützenberger representation theorem (formal language theory) Choquet–Bishop–de Leeuw theorem (functional analysis)
This is the form of the remainder term mentioned after the actual statement of Taylor's theorem with remainder in the mean value form. The Lagrange form of the remainder is found by choosing () = + and the Cauchy form by choosing () =. Remark.
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.
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