In math-speak:

A polynomial A(x) = a0 + a1x + a2x2 + a3x3 + ... may be written as A(x) = a0 + x(a1 + x(a2 + x(a3 + ...))).

In english:

(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.

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