On dividing $^{3}+6 z+4 z^{5} $by $ 2 z-1 $, the quotient obtained is a and the remainder is b.

What are the values of a and b?

A) $ a=2 z^{4}-z^{3}+z^{2}-\frac{z}{2}+\frac{13}{4} \ and \ b=-\frac{13}{4} $

B) $ a=2 z^{4}+z^{3}+z^{2}+\frac{z}{2}+\frac{13}{4} \ and \ b=\frac{13}{4} $

C) $ a=2 z^{4}-z^{3}+\frac{z^{2}}{2}+\frac{z}{4}+\frac{23}{8} \ and \ b=-\frac{23}{8} $

D) $ a=2 z^{4}+z^{3}+\frac{z^{2}}{2}+\frac{z}{4}+\frac{23}{8} \ and \ b=+\frac{23}{8} $

On dividing $z^{3} + 6 z + 4 z^{5}$  by 2 z − 1 , the quotient obtained is a and the remainder is b.

$2z- 1$ | $4 z^{5} + z^{3} + 6 z$ | $2z^{4} + z^{3} + z^{2} + \frac{z}{2} +\frac{13}{4}$

                $4z^{5} - 2z^{4}$

                --------------

                $2z^{4} + z^{3}$

                $2z^{4} - z^{3}$

              - -------------

                $2z^{3} + 6z$   

                $2z^{3} - z^{2}$

               --------------

                $z^{2} + 6z$

                $z^{2} - \frac{z}{2}$

              ---------------

             $\frac{13z}{2}$

             $\frac{13z}{2} - \frac{13}{4}$

             ----------------

              $\frac{13}{4}$  

Option A is wrong. Option B is correct

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Updated on: 10-Oct-2022

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