You did not actually go wrong, but your method is not the one you are tested on. I'm not sure you understood what your tutor is saying. You need to use the factor theorem as demonstrated below:
Basically you should look for a root in your original polynomial. x³ + x² - 4x - 4
For example, as your tutor has noted, so is a factor of .
Now dividing by , you get
Set and observe that . Therefore is a factor of . Dividing by gives . That is, . Hence