Division de polynômes

Effectuer les divisions suivantes:

Clear[x];
For[i = 1, 
      i < 11, 
a = 
        Random[Integer, {-3, 3}]; 
b = 
        Random[Integer, {-3, 3}]; 
c = 
        Random[Integer, {-2, 2}]; 
d = 
        Random[Integer, {-3, 3}]; 
e = 
        Random[Integer, {-4, 4}]; 
f = 0; 
      While[f == 0, 
f = 
          Random[Integer, {-3, 3}]]; 
quotient[i] =  
        a x^4 + b x^3 + c x^2  + d x + e; 
diviseur[
          i] =  x  -  f; 
reste[i] = 
        Random[Integer, {-12, 12}]; 
dividende[i] = 
        Expand[quotient[i]*diviseur[i] + reste[i]]; 
Print[
        i, ") diviser A(x) = ", dividende[i],  "   par B(x) = ", 
        diviseur[i]]; 
i++]

CellPrint[Cell["Solutions :", "Subsubtitle"]]

Solutions :

For[i = 1, i < 11, 
      Print[i, ")  A(x) = ", 
        diviseur[i]*quotient[i] + reste[i]]; i++]