;;A polynomial is expressed in list form. 1+3x+5x^2+7x^3 would be entered as '(1 3 4 7)


(define (nzero n) ;;Returns a list of n zeros
  (if (< n 1) '()
      (cons 0 (nzero (- n 1)))))

(define (polyAdd p1 p2) ;;adds two polynomials expressed in lists
  (if (null? p1) p2 (if (null? p2) p1
   (cons (+ (car p1) (car p2)) (polyAdd (cdr p1) (cdr p2))))))

(define (polyAddList l) ;;adds a list of polynomials expressed in lists
  (if (null? l) '()
  (polyAdd (car l) (polyAddList (cdr l)))))


;;returns a list of lists
;;used to find the product of a polynomial by adding these lists:
(define (polyMultHelper l1 l2 n)
   (if (null? l1) '()
   (cons (append (nzero n) (map (lambda (x) (* (car l1) x)) l2))
         (polyMultHelper (cdr l1) l2 (+ n 1)))))

(define (polyMult p1 p2) ;;returns the product of two polynomials
  (polyAddList (polyMultHelper p1 p2 0))) ;;WHAT SHOULD THIS n BE INSTEAD OF 0??