5x3+x2-3x+7 divided by x-1 (long division)

Question

(long division) 

Answer 1

 

          5x² + 6x + 3

x-1  |  5x³ +x² - 3x + 7

         -(5x³ -5x²)

                 6x² - 3x

               - (6x² - 6x)

                         3x + 7

                       -(3x -3)

                              10

 

5x² + 6x + 3  + 10/x-1

 

I have seen some people want to introduce mod into an answer.  I think that this answer should be sufficient for most teachers and makes the answer easy to understand.