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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