### In math-speak:

A polynomial `A(x) = a`_{0} + a_{1}x + a_{2}x^{2} + a_{3}x^{3} + ... may be written as `A(x) = a`_{0} + x(a_{1} + x(a_{2} + x(a_{3} + ...))).

(well, mostly English)

A polynomial may be evaluated at a point x', that is A(x') computed, in Θ^{*} time using Horner's rule. That is, repeated multiplications and additions, rather than the naive methods of raising x to powers, multiplying by the coefficient, and accumulating.

^{*} Θ (Theta) is commonly used as a symbol signifying the execution of an algorithm, usually in terms of

time or

memory required.