Evaluating a polynomial in x at a given value of x can be formulated as an accumulation. We evaluate the polynomial
using a well-known algorithm called Horner's rule, which structures the computation as
In other words, we start with aₙ, multiply by x, add aₙ₋₁, multiply by x, and so on, until we reach a₀. Fill in the following template to produce a procedure that evaluates a polynomial using Horner's rule. Assume that the coefficients of the polynomial are arranged in a sequence, from a₀ through aₙ.
(define (horner-eval x coefficient-sequence) (accumulate (lambda (this-coeff higher-terms) <??>) 0 coefficient-sequence))
For example, to compute 1 + 3x + 5x³ + x⁵ at x = 2 you would evaluate
(horner-eval 2 (list 1 3 0 5 0 1))
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(check-equal? (horner-eval 1 (list 1 3 0 5 0 1)) 10) (check-equal? (horner-eval 2 (list 1 3 0 5 0 1)) 79) (check-equal? (horner-eval 2 (list 1 3 1 5 0 1)) 83)