Definition:Ruffini-Horner Method

Definition
The Ruffini-Horner method is a technique for finding the roots of polynomial equations in $1$ real variable.

Let $E_0$ be the polynomial equation in $x$:
 * $\map p x = 0$

Suppose that a root $x_0$ being sought is the positive real number expressed as the decimal expansion:
 * $x_0 = \sqbrk {abc.def}$

The process begins by finding $a$ by inspection.

We then form a new equation $E_1$ whose roots are $100 a$ less than those of $E_0$.

This will have a root $x_1$ in the form:
 * $x_1 = \sqbrk {bc.def}$

Similarly, $b$ is found by inspection.

We then form a new equation $E_2$ whose roots are $10 b$ less than those of $E_1$.

The process continues for as many digits accuracy as required.