def calcuter(P,x):
    P=P[::-1]
    u=P[0]
    for k in range (1,len(P)):
        u=x*u+P[k]
    print (u)


#Q4 a)
def derive(A):
    Aderiv=[]
    for k in range(len(A)):
        Aderiv=Aderiv+[k*A[k]]
    return (Aderiv)

#Q4 b)
def multiplicite(P,x):
    m=0
    while calcuter(P,x)==0:
        P=derive(P)
        m=m+1
        return(m)