Ruffini-Horner Method for a Polynomial in Powers of x-h

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This Demonstration shows the transformation of a polynomial in powers of into a polynomial in powers of
using the Ruffini–Horner method.
Contributed by: Izidor Hafner (December 2016)
Open content licensed under CC BY-NC-SA
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Given a polynomial
,
find a way to express it as a polynomial in :
.
One method is to use a Taylor series
.
Another way is to make use of synthetic division, discovered by Ruffini in 1804 and Horner in 1819.
References
[1] Wikipedia. "Paolo Ruffini." (Dec 12, 2016) en.wikipedia.org/wiki/Paolo_Ruffini.
[2] Wikipedia. "William George Horner." (Dec 12, 2016) en.wikipedia.org/wiki/William_George_Horner.
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