Question

HURRY............PLEASE..............divide the polynomial x4-11x2+34x-12 by x-2 and find the quotient and remainder . also verify the division algorithm

Answer 1

Given f(x) = x^4 - 11x^2 + 34x - 12.

Given g(x) = x - 2.

Now, we need to divide f(x) by g(x).


          x^3 + 2x^2 - 7x + 20
        -----------------------------------
x - 2) x^4          - 11x^2 + 34x - 12

         x^4 - 2x^3

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

                  2x^3 - 11x^2 + 34x - 12

                  2x^3 - 4x^2

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

                             -7x^2 + 34x - 12

                             - 7x^2 + 14x - 12

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

                                           20x - 12

                                           20x -40

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

                                                   28


We know that Dividend = Divisor * Quotient + Remainder

 = > (x - 2) * (x^3 + 2x^2 - 7x + 20) + 28

= > x^4 + 2x^3 - 7x^2 + 20x - 2x^3 - 4x^2 + 14x - 40 + 28

= > x^4 - 11x^2 + 34x - 12

= > Dividend



Hope this helps!

Answer 2

Quotient =x^3+2x^2-7x+20
Remainder =28

hence verified ( pic 2 )