Question

By long division, find the quotient and remainder, when the polynomial
2x4 -5x3+3x-1 is divided by 2x-1.

Answer 1

GIVEN :

By long division, find the quotient and remainder, when the polynomial

is divided by 2x-1.

TO FIND :

The quotient and remainder, when the polynomial  $2x^4-5x^3+3x-1$ is divided by 2x-1 by using Long Division Method

SOLUTION :

Given that when the polynomial  $2x^4-5x^3+3x-1$ is divided by 2x-1.

By using the Long Division Method we can solve the polynomial as below :

For our convenience, we can write the given polynomial $2x^4-5x^3+3x-1$ as $2x^4-5x^3+0x^2+3x-1$

             $x^3-2x^2-x+1$

           ______________________

    2x-1 ) $2x^4-5x^3+0x^2+3x-1$

              $2x^4-x^3$

             (-)___(+)__________

                       $-4x^3+0x^2$

                       $-4x^3+2x^2$

                      _(+)__(-)____________

                                  $-2x^2+3x$

                                  $-2x^2+x$

                                 _(+)___(-)________

                                            2x-1

                                            2x-1

                                         _(-)_(+)____

                                                 0

                                        __________

When the given polynomial $2x^4-5x^3+3x-1$ is divided by 2x-1 by using Long Division Method we have that the remainder is 0 and the quotient is $x^3-2x^2-x+1$

∴ Quotient=$x^3-2x^2-x+1$ and Remainder=0