Method of Newton-Raphson along with Horner

I'm having trouble implementing Horner's method to decrease the computational cost of polynomial calculations, and doing so use Newton's method to find the root of the polynomial

In the code, b would store the value of the polynomial and c the value of the derivative

n=len(a)-1
print("k\ta\tx\tpx")
for k in range (1, iterMax):
    b=a[n] 
    c=0
    for i in range (n-1,1):
        c=b-(x*c)
        b=(x*b)+a[i]
    b=x*b+a[0]
    if (b<epsilon and b>-epsilon):
        print ("raiz encontrada: ")
        print (x)
        return (0, x)
    x=x-(b/c)   
print("erro. Maximo de interações atingido") 
return (1, x)

When you apply Newton's method (x = x- (b / c)), you acknowledge error saying that I am dividing by zero, but I do not understand why.

Function call:

a = [3, -9, 0, 1]
x0 = 0.5
epsilon = 0.0001
maxIter = 20
(houveErro, raiz) = newton_poli(a, x0, epsilon, maxIter)

Note: as I understand it, the list stores the coefficients backwards, that is, 3 is the independent term and 1 is the multiplying term x³