If $x^{2}$ + x + 1 is a factor of the polynomial $3 x^{3} + 8 x^{2}$ + 8x + 3 + 5k, then the value of k is

$\frac{2}{3}$

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$\frac{2}{5}$

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$\frac{5}{2}$

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$\frac{3}{2}$

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Solution

The correct option is B
$\frac{2}{5}$

f(x) $3 x^{3} + 8 x^{2} + 8 x + 3 + 5 k$

Now dividing by $x^{2} + x + 1$ , we get

$∵$ 3 + 5k - 5 is a remainder

$∴$ Remainder is zero

$∴$ 3 + 5k - 5 = 0 $\Rightarrow$ 5k - 2 = 0

$\Rightarrow 5 k = 2 \Rightarrow k = \frac{2}{5}$

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