How does Horner’s method work?
In mathematics, Horner’s method (also known as Horner scheme in the UK or Horner’s rule in the U.S.) is either of two things:
an algorithm for calculating polynomials, which consists of transforming the monomial form into a computationally efficient form; or
a method for approximating the roots of a polynomial.
The latter is also known as Ruffini–Horner’s method.
These methods are named after the British mathematician William George Horner, although they were known before him by Paolo Ruffini and, six hundred years earlier, by the Chinese mathematician Qin Jiushao.