Horner's rule


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

Note: A polynomial may be evaluated at a point x', that is A(x') computed, in Θ(n) 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.

Author: PEB

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Entry modified 17 December 2004.
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Cite this as:
Paul E. Black, "Horner's rule", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed. 17 December 2004. (accessed TODAY) Available from: