Question 1127861
<br>
Remember that "complex numbers" includes real numbers.  So look for rational roots first.<br>
Substitution show f(-1)=0, so -1 is a root.  Extract that root using synthetic division.<br><pre>

   -1 |  1 -1  0 -2 -4
      |    -1  2 -2  4
      ----------------
        1  -2  2 -4  0
</pre>
The remaining polynomial is {{{x^3-2x^2+2x-4}}}.  A second real root can be found using factoring by grouping.<br>
{{{x^3-2x^2+2x-4 = (x^3-2x^2)+(2x-4) = x^2(x-2)+2(x-2) = (x^2+2)(x-2)}}}<br>
The remaining quadratic factor can be factored over the complex numbers as<br>
{{{(x+i*sqrt(2))(x-i*sqrt(2))}}}<br>
So the complete factorization over the complex numbers is<br>
{{{x^4-x^3-2x-4 = (x+1)(x-2)(x+i*sqrt(2))(x-i*sqrt(2))}}}