Question 427352
  <pre><font face = "Tohoma" size = 4 color = "indigo"><b>
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