Question 595715
{{{X^3+2X^2-33X-90}}}
To find the other factors we start by dividing by the known factor, x+5. I prefer synthetic division over long division:
<pre>
-5 |   1   2   -33   -90
---       -5    15    90
     --------------------
       1  -3   -18     0
</pre>
The remainder, in the lower right corner, is zero. This is to be expected when x+5 was supposed to be a factor. The other factor is found in the front of the remainder: 1 -3 -18. This translates into {{{x^2 -3x - 18}}}. Now we just factor that:
{{{x^2-3x-18 = (x-6)(x+3)}}}<br>
So your expression, fully factored, is:
{{{X^3+2X^2-33X-90 = (x+5)(x-6)(x+3)}}}