Question

What must be subtracted from the polynomial f(x)=x4 +2x3-13x2 -12x+21 , so that the resulting polynomial is exactly divisible by x2-4x+3?

Answer 1

Answer:

2x-3

Step-by-step explanation:

x2-4x+3) x4 + 2x3 - 13x2 - 12x + 21 (x2 + 6x + 8

               x4 - 4x3 + 3x2

            (-)    (+)      (-)

                      6x3 - 16x2 - 12x + 21

                      6x3 - 24x2 + 18x

                  (-)      (+)         (-)

                                8x2 - 30x + 21

                                8x2 - 32x + 24

                            (-)      (+)       (-)

                                          2x - 3

Hence the remainder i.e 2x-3 should be subtracted from the Polynomial f(x), so that the resulting polynomial is exactly divisible by x2-4x+3.