When $3 x^{3} + 2 x^{2} + 2 x + k$ is divided by $x + 2$ , the remainder is $4$ . Calculate the value of $k$ .

4

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24

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34

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54

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Solution

The correct option is B $24$
Given the equation $3 x^{3} + 2 x^{2} + 2 x + k$ is divided by $x + 2$ the reminder is $4$ .
Put the value $x = - 2$ in equation, we get
$3 (- 2)^{3} + 2 (- 2)^{2} + 2 (- 2) k = 4$
$\Rightarrow 3 (- 8) + 2 (4) + 2 (- 2) + k = 4$
$\Rightarrow - 24 + 8 - 4 + k = 4$
$\Rightarrow k = 4 + 24 - 8 + 4$
$\Rightarrow k = 24$

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