Using long division method, divide the polynomial
$4 p^{3} - 4 p^{2} + 6 p - \frac{5}{2}$ by $2 p - 1$

2 p^{2} - p - \frac{5}{2}

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2 p^{2} + p + \frac{5}{2}

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2 p^{2} - p + \frac{5}{2}

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None of the above

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Solution

The correct option is C $2 p^{2} - p + \frac{5}{2}$
$2 p^{2} - p + \frac{5}{2}$
$2 p - 1$ $4 p^{3} - 4 p^{2} + 6 p - \frac{5}{2}$
$4 p^{3} - 2 p^{2}$
$- 2 p^{2} + 6 p - \frac{5}{2}$
$- 2 p^{2} + p$
$5 p - \frac{5}{2}$
$5 p - \frac{5}{2}$
$0$
$(4 p^{3} - 4 p^{2} + 6 p - \frac{5}{2}) \div$ $(2 p - 1) = 2 p^{2} - p + \frac{5}{2}$

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