# 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

## Snapshots

## Details

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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