By long division, find the quotient and remainder, when the polynomial 2×4 -5×3+3x-1 is divided by 2x-1.

Question

By long division, find the quotient and remainder, when the polynomial
2×4 -5×3+3x-1 is divided by 2x-1.

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Ariana 2 months 2021-09-10T18:33:55+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-09-10T18:35:38+00:00

    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

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