Question

what should be added to the polynomial x^3-6x^2+11x+8 so that it is completely divisible by x^2-3x+2

Answer 1

Sol:
Given polynomial x3 - 3x2 - 12x + 19

                        x2 + x - 6 ) x3 - 3x2 - 12x + 19  ( x - 4
                                        x3 + x2 - 6x ( substract)
                                       ----------------------------
                                            - 4x2 - 6x + 19
                                            - 4x2 - 4x + 24  ( substract)
                                       ----------------------------
                                                    - 2x - 5

Here remainder is - 2x - 5 . 2x + 5  must be added to x3 - 3x2 - 12x + 19, so that result is exactly divisible by x2 + x - 6.