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If $k x^{3} + 9 x^{2} + 4 x - 8$ is divided by $(x + 3)$ the remainder is $- 20$ , then the value of $k$ is

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Detailed Solution

$f (x) = k x^{3} + 9 x^{2} + 4 x - 8$

Given $f (- 3) = - 20$

$\Rightarrow k {(- 3)}^{3} + 9 \times {(- 3)}^{2} + 4 (- 3) - 8$ $= - 20$

$\Rightarrow - 27 k + 81 - 12 - 8$ $= - 20$

$\Rightarrow k = \frac{- 81}{- 27}$ $= 3$

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