Horner's Method

Horner’s method is an efficient algorithm for evaluating a Polynomial by factoring out $x$ repeatedly, eliminating the need to compute powers of $x$ directly.

For example, a cubic polynomial:

$$p(x)=a_3{x}^3+a_2{x}^2+a_{1}x+a_0$$

is evaluated as:

$$p(x)=((a_3\cdot x+a_2)\cdot x+a_1)\cdot x+a_0$$