sicp-all-tasks/sicp/2_002e34

Exercise 2.34: Evaluating a polynomial in 
  x

at a given value of 
  x
 can be formulated as an accumulation.  We evaluate
the polynomial

  
    
      a
      n
    
    
      x
      n
    
  
  +
  
    
      a
      
        n
        −
        1
      
    
    
      x
      
        n
        −
        1
      
    
  
  +
  ⋯
  +
  
    
      a
      1
    
    x
  
  +
  
    a
    0
  

using a well-known algorithm called 
Horner’s rule, which structures
the computation as

  
    (
    …
    (
    
      a
      n
    
    x
  
  +
  
    
      a
      
        n
        −
        1
      
    
    )
    x
  
  +
  ⋯
  +
  
    
      a
      1
    
    )
    x
  
  +
  
    
      a
      0
    
    .
  

In other words, we start with 
  
    a
    n
  
, multiply by 
  x
, add

  
    a
    
      n
      −
      1
    
  
, multiply by 
  x
, and so on, until we reach

  
    a
    0
  
.82

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 
  
    a
    0
  
 through 
  
    a
    n
  
.


(define 
  (horner-eval x coefficient-sequence)
  (accumulate 
   (lambda (this-coeff higher-terms)
     ⟨??⟩)
   0
   coefficient-sequence))

For example, to compute 
  
    1
    +
    3
    x
  
  +
  
    5
    
      x
      3
    
    +
    
      x
      5
    
  
 at 
  
    x
    =
    2
  
 you
would evaluate


(horner-eval 2 (list 1 3 0 5 0 1))