Hi

As to checking the answer: 

Note:

  1) (x-1) is a factor as when x=1, then f(1)= 1+2+3-6= 0



  (x^3+2x^2+3x-6)/(x-1)= x^2 + 3x + 6  

  2) checking the result of the division could be done by showing:

      (x-1)(x^2 + 3x + 6) =  x^3+2x^2+3x-6



          x^2 + (3x) +   6

        __________________________

x - 1 | x^3  +2x^2   +3x   -6      

      - (x^3 -x^2)

       ---------------

               3x^2 + 3x

             - (3x^2 -3x))

                --------------

                      6x - 6

                   - (6x - 6)

                          --------

                            0

 

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