Newton-Raphson method together with Horner

Question

I’m having trouble implementing Horner’s method to decrease the computational cost of polynomial calculations and, having done so, using 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 applying the Newton method (x=x-(b/c)), it accuses 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: from what I understand, the list a stores the coefficients backwards, that is, 3 is the independent term and 1 is the term that multiplies x³