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



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.


[1] Wikipedia. "Paolo Ruffini." (Dec 12, 2016)

[2] Wikipedia. "William George Horner." (Dec 12, 2016)

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