Thank you for your answer. I have testet it, and the result is not the expected one (output #8). Please can you help me, thanks.
In[1]:= x {1, 3}
Out[1]= {x, 3 x}
In[2]:= expr = {a x + b x^2, c x + d x + 3 x^2}
Out[2]= {a x + b x^2, c x + d x + 3 x^2}
In[3]:= expr = Factor /@ expr
Out[3]= {x (a + b x), x (c + d + 3 x)}
In[4]:= divisors =
If[MatchQ[#, Times[_]], Cases[#, Times[x] :> x], {1}] & /@ expr
Out[4]= {{x, a + b x}, {x, c + d + 3 x}}
In[5]:= common = Times @@ Intersection @@ divisors
Out[5]= x
In[6]:= expr /= common
Out[6]= {a + b x, c + d + 3 x}
In[7]:= expr = Inactivate[common expr]
Out[7]= Inactivate[{x (a + b x), x (c + d + 3 x)}]
In[8]:= expr // Activate
Out[8]= Activate[Inactivate[{x (a + b x), x (c + d + 3 x)}]]