Question 377533
<pre>

         x^2 + x - 6
        __________________________
 x + 1 | x^3 +  2x^2 -  5x - 6
      - (x^3 +   x^2)
       ---------------
                 x^2 -  5x  
             -  (x^2 +   x)
                --------------
                       -6x - 6 
                   -  (-6x - 6) 
                      ---------
                             0
</pre>
{{{ (x^3+2x^2-5x-6)/(x+1) =(x^2+x-6)}}}
Since the remainder is zero, {{{(x+1)}}} is a factor.
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<pre>

         x^2 + 5x + 10
        __________________________
 x - 3 | x^3 +  2x^2 -  5x -  6
      - (x^3 -  3x^2)
       ---------------
                5x^2 -  5x  
             - (5x^2 - 15x)
                ---------------
                       10x -  6 
                   -  (10x - 30) 
                      ----------
                             24
</pre>
{{{ (x^3+2x^2-5x-6)/(x-3) =(x^2+5x+10)+24/(x-3)}}}
Since the remainder is not zero, {{{(x-3)}}} is not a factor.
.
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