Divide and verify the following
$15 x^{3} - 20 z^{2} + 13 z + 12$ by $(3 z - 6)$

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Solution

$\begin{matrix} Q u o t i e n t = 5 z^{2} + \frac{10}{3} z + 11 R e m a i n d e r = 78 D i v i d e n d = 15 z^{3} - 20 z^{2} + 13 z + 12 D i v i s o r = z - 6 d i v i s o r \times q u o t i e n t + r e m a i n d e r = (3 z - 6) \times (5 z^{2} + \frac{10}{3} z + 11) + 78 \Rightarrow 15 z^{3} + 10 z^{2} + 33 z - 30 z^{2} - 20 z - 66 + 78 \Rightarrow 15 z^{3} - 20 z^{2} + 13 z + 12 = d i v i d e n d H e n c e, v e r i f i e d \end{matrix}$

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