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From: Axel Vogt on 13 Sep 2009 15:24
Bráulio Bezerra wrote:
> Hi,
>
> Virtually every kid in Brazil learns to divide polynomials by one of
> the form (x - a) using the Briot-Ruffini method. It is just a long
> division method, but works a little faster since someone writes only
> the coefficients. It also has numerical applications, since it can be
> used to find the value of a polynomial and its derivatives of all
> orders at some given point, in a particularly efficient way. This is
> done viewing the polynomial as (((a_4x + a_3) x + a_2) x + a_1 ) x +
> a_0, for example.
>
> The problem is that this method is only mentioned by Brazilian people
> in books, on the Internet, everywhere. So I don't know if this method
> is so obvious that it commonly deserves no mention; if this is just a
> trend we have in Brazilian education; or if it has another name
> outside Brazil.
>
> Any thoughts, anyone?

http://en.wikipedia.org/wiki/Horner_scheme (though I never liked
such a representation, Chip Eastman's answer shows the essence).
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