Horner's rule

Etymology
Named after William George Horner, though it significantly pre-dates his work.

Proper noun
a_0 &+ a_1x + a_2x^2 + a_3x^3 + \cdots + a_nx^n \\ &= a_0 + x \bigg(a_1 + x \Big(a_2 + x \big(a_3 + \cdots + x(a_{n-1} + x \, a_n) \cdots \big) \Big) \bigg). \end{align}$$
 * 1)  The rule stating that a polynomial of degree n can be (optimally) evaluated with only n multiplications and n additions: $$\begin{align}