Divide $10 x^{3} + 19 x^{2} + 12 x - 9$ by $2 x - 3$

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Solution

$(2 x - 3) 10 x^{3} + 19 x^{2} + 12 x - 9 (5 x^{3} + 17 x + \frac{63}{2})$
$10 x^{3} - 15 x^{2}$
- +
______
$34 x^{2} + 12 x$
$34 x^{2} - 51 x$
- +
_
$63 x - 9$
$63 x - \frac{63 \times 3}{2}$
- +

$\frac{171}{2}$
___
$∴$ quotient : $5 x^{2} + 17 x + \frac{63}{2}$
remainder : $\frac{171}{2}$

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