Horner's method

Summary

Horner's method evaluates a polynomial of degree $n$ with $n$ multiplications and $n$ additions. It rewrites $a_n x^n + \dots + a_0$ as a nested product $a_0 + x(a_1 + x(a_2 + \dots + x a_n))$. The intermediate values are the coefficients of the quotient by $x - c$, so it also performs synthetic division. It is the standard way to carry out polynomial evaluation.