If $x^{4} - 9 x^{3} - 2 x^{2} + 6 x - 8$ is divided by $x - 3,$ then the remainder is ___________.

- 180

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- 170

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- 160

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- 150

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Solution

The correct option is B $- 170$
$(x^{4} - 9 x^{3} - 2 x^{2} + 6 x - 8) = (x - 3) (x^{3} - 6 x^{2} - 20 x - 50) = - 170$
$∴$ Remainder $= - 170$

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