Question 1113622
The possible roots to test are  -12, -6, -4, -3, -2, -1, 1, 2, 3, 4, 6, 12.


The roots will be found -3, -2, -1, 2.
You could use synthetic division to check each possible root and continue with the resulting quotient, to continue checking for the possible roots.



Just one example.
<pre>
-3  |  1   4   -1   -16   -12
    | 
    |     -3   -3    12    12
    |------------------------------
      1   1   -4    -4     0
</pre>
Remainder of 0;
The next polynomial to check roots of is  {{{x^3+x^2-4x-4}}}
but now the possible roots to check are now -4,-2,-1,1, 2, 4.  


All the roots found will be -3, -2, -1, 2.