Question

what must be subtracted from (x^4+2x^3-2x^2+4x+6) so that the result is exactly divisible by (x^2+2x-3)?

pls answer fast to get points.

Answer 1

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Answer 2

Let p(x) = x^4 + 2x^3 - 2x^2 + 4x + 6

Let g(x) = x^2 + 2x - 3.

We need to divide f(x) by g(x).


                           x^2  +   1
                      -----------------------------------------------
x^2 + 2x - 3)  x^4   +  2x^3   -  2x^2   +  4x   +  6

                      x^4   +  2x^3   -   3x^2

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

                                                       x^2  +  4x  +  6

                                                       x^2   +  2x  - 3

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

                                                                    2x  +  9.




Thus, the expression x^4 + 2x^3 - 2x^2 + 4x + 6 is exactly divisible by x^2 + 2x - 3 when 2x + 9 is subtracted from it.




Hope this helps!