Question

what must be subtracted from 8x^4+14x^3 - 2x^2 +7x-8 so that the resulting polynomial is exactly divisible by (4x^2 +3x-2)?

Answer 1

Hope this helps you...

Answer 2

Answer:

14x - 10 should be subtracted from the given polynomial  

Step-by-step explanation:

p(x)=   8x^4 + 14x^3 - 2x^2 +7x - 8       g(x)=  4x^2 +3x-2    

4x^2 +3x-2 ) 8x^4 + 14x^3 - 2x^2 +7x - 8 ( 2x^2 + 2x - 1

                               -  8x^4 + 6x^3 - 4x^2

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

                                      0   + 8x^3 + 2x^2 + 7x

                                  --       + 8x^3 + 6x^2  - 4x

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

                                                0     - 4x^2 + 11x - 8

                                        +              - 4x^2  - 3x + 2

                                 _____________________

                                                          0        + 14x -10

r(x) = 14x -10

Here we must divide the polynomial p(x) with the one which will exactly divide the new polynomial g(x). Then the remainder r(x) must subtracted from p(x).