Question

Divide p(x)= 2x4+13x2-7x3-11x+5 by g(x) = 3+x2-2x and also verify the division Algorithm

Answer 1

Answer:

Step-by-step explanation:

Given  

Divide p(x)= 2x4+13x2-7x3-11x+5 by g(x) = 3+x2-2x and also verify the division Algorithm

ANSWER

x^2 – 2 x + 3)2x^4 – 7 x^3 + 13 x^2 – 11 x + 5 (2 x^2 – 3 x + 1

                    2x^4 – 4 x^3 + 6x^2

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

                             -3x^3 + 7x^2 – 11 x

                              -3x^3 + 6x^2 – 9 x   subtracting

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

                                            x^2 – 2 x + 5

                                            x^2 – 2 x + 3 subtracting

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

                                                                2

Now quotient = 2 x^2 – 3 x + 1 and remainder = 2

We know that to verify  

Dividend = quotient x divisor + remainder

                = (2 x^2 – 3 x + 1)(x^2 – 2 x + 3) + 2

               = 2 x^4 – 3 x^3 + x^2 – 4 x^3 + 6 x^2 – 2 x + 6 x^2 – 9 x + 3 + 2

                 = 2 x^4 – 7 x^3 + 13 x^2 – 7 x^3 – 11 x + 5 (verified)