Create polynomial function - racket

Question

In my test I was asked to write a function createPolynomial that
takes as arguments a list of 𝑘 numbers 𝑎0, … , 𝑎𝑘−1 and returns as output a
function. The returned function takes a number 𝑥0 and return the value of
the polynomial 𝑎0 ⋅ 𝑥0 + ⋯ + 𝑎𝑘−1 ⋅ 𝑥𝑛−1 at 𝑥0. To this end, I used the
built-in pl expt function taking two numbers 𝑎 and 𝑏, and returning 𝑎^𝑏
i was given a partial code which I will post down below with my answer and wanted to test my answer at home but I can't make it run although my teacher marked my answer as correct. Any help would be appreciated
here is the partial code:
(: createPolynomial : (Listof Number) -> <-fill in->)
(define (createPolynomial coeffs)
(: poly : (Listof Number) Number Integer Number ->
Number)
(define (poly argsL x power accum)
(if <-fill in->
<-fill in->
<-fill in-> )
(: polyX : Number -> Number)
(define (polyX x)
fill in)
fill in)
And here is my answer:
(: createPolynomial : (Listof Number) -> (Number -> Number))
(define (createPolynomial coeffs)
(: poly : (Listof Number) Number Integer Number ->
Number)
(define (poly argsL x power accum)
(if (null? argsL)
accum)
(poly (rest argsL) x (+ power 1) (+ accum (* (first argsL) (expt x power)))))
(: polyX : Number -> Number)
(define (polyX x)
(poly coeffs x 0 0)
polyX x))
and here are some test for the code:
> (createPolynomial '(1 2 4 2))
- : (Number -> Number)
#<procedure:polyX>
(define p2345 (createPolynomial '(2 3 4 5)))
(test (p2345 0) =>
(+ (* 2 (expt 0 0)) (* 3 (expt 0 1)) (* 4 (expt 0 2)) (* 5
(expt 0 3))))
(test (p2345 4) =>
(+ (* 2 (expt 4 0)) (* 3 (expt 4 1)) (* 4 (expt 4 2)) (* 5
(expt 4 3))))
(test (p2345 11) => (+ (* 2 (expt 11 0)) (* 3 (expt 11 1)) (* 4
(expt 11 2)) (* 5 (expt 11 3))))
(define p536 (createPolynomial '(5 3 6)))
(test (p536 11) => (+ (* 5 (expt 11 0)) (* 3 (expt 11 1)) (* 6
(expt 11 2))))
(define p_0 (createPolynomial '()))
(test (p_0 4) => 0)
I'm getting the error -
define: empty body (after defns/decls) in: (define (createPolynomial coeffs) (: poly : (Listof Number) Number Integer Number -> Number) (define (poly argsL x power accum) (if (null? argsL) accum) (poly (rest argsL) x (+ power 1) (+ accum (* (first argsL) (expt x power))))) (: polyX : Number -> Number) (define (polyX x) (poly coeffs x 0 0) polyX x))
>

Answer 1

An empty means that the there are no expressions in the body.
Usually it means a parenthesis is misplaced.
Use indentation!
I am guessing, you meant to write:
(: createPolynomial : (Listof Number) -> (Number -> Number))
(define (createPolynomial coeffs)
(: poly : (Listof Number) Number Integer Number ->
Number)
(define (poly argsL x power accum)
(if (null? argsL)
accum)
(poly (rest argsL) x (+ power 1) (+ accum (* (first argsL) (expt x power)))))
(: polyX : Number -> Number)
(define (polyX x)
(poly coeffs x 0 0))
(polyX x))

Answer 2

The answer above didn't help me (cus I'm writing in pl)
So this is my solution:
(: createPolynomial : (Listof Number) -> (Number -> Number))
(define (createPolynomial coeffs)
(: poly : (Listof Number) Number Integer Number -> Number)
(define (poly argsL x power accum)
(if (null? argsL)
accum
(poly (rest argsL) x (+ power 1) (+ accum (* (first argsL) (expt x power)))) ))
(: polyX : Number -> Number)
(define (polyX x)
(poly coeffs x 0 0))
polyX
)
You call the polyX (that is a Num -> Num) as the return of "createPolynomial".
So when calling (in some define) createPolynomial with a list of numbers then you call again to what you define with a number, that number will go into polyX that will use the list and x to create the poly function.