Question 1138587
The possible roots to check for would be  -6, -3, -2, -1, 1, 2, 3, 6.
Using synthetic division to test should indicate 3 and -1 to be the rational roots.


Two more roots to find for the quadratic part left over from the two synthetic divisions (could be two irrational zeros).

<pre>
3  |  1   -2   -5   4   6
   |       3    3  -6   -6
   |___________________________
     1    1    -2  -2   0


-1  |   1   1   -2   -2
    |
    |      -1   0     2
    |________________________
        1  0    -2    0
</pre>
{{{(x^2-2)^2=0}}}

{{{x^2-2=0}}}

{{{x^2=2}}}

{{{system(x=-sqrt(2),x=sqrt(2),the_last_two_roots)}}}