Help a question regarding factor theroem

So f(x) = x²+(7/3)x +2/3. And g(x)=xf(2x) - f(x-(1/3))+2x/3 and need to find factors of gx without evaluvating f(2x) or f(x - 1/3) I have no clue how i am even supposed to approach this problem. First part of the question is prove that there are two real negative roots to fx and i did that.i tried substituting a variable call m that is a root of gx and subjected m but i ain getting anyware..