A fast scheme for evaluating a polynomial such as:
: <math>-19+7x-4x^2+6x^3\,</math>
when
: <math>x=3\;</math>.
is to arrange the computation as follows:
: <math>((((0) x + 6) x + (-4)) x + 7) x + (-19)\;</math>
And compute the result from the innermost brackets outwards as in this pseudocode:
 coefficients ''':=''' [-19, 7, -4, 6] ''# list coefficients of all x^0..x^n in order''
 x ''':=''' 3
 accumulator ''':=''' 0
 '''for''' i '''in''' ''length''(coefficients) '''downto''' 1 '''do'''
     ''# Assumes 1-based indexing for arrays''
     accumulator ''':=''' ( accumulator * x ) + coefficients[i]
 '''done'''
 ''# accumulator now has the answer''

'''Task Description'''
:Create a routine that takes a list of coefficients of a polynomial in order of increasing powers of x; together with a value of x to compute its value at, and return the value of the polynomial at that value using [http://www.physics.utah.edu/~detar/lessons/c++/array/node1.html Horner's rule].

Cf. [[Formal power series]]
