Horner's method for computing a polynomial both reduces the number of multiplications and results in greater numerical stability by potentially avoiding the subtraction of large numbers. It is based on successive factorization to eliminate powers of greater than 1.
Suppose ; then the method rewrites .
To compute , we find
The factor polynomial is given by .
You can select , the degree of the polynomial; , the desired value at ; and , the number of steps in which is replaced by . The table shows the new coefficients after each step.