If $x + 2$ is factor of $(x + 1)^{5} + (2 x + K)^{3}$ , then the value of $^{'} K^{'}$ is

1

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3

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4

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5

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Solution

The correct option is D $5$
If $x + 2$ is a factor of $f (x) = (x + 1)^{5} + (2 x + K)^{3}$ , then
$f (- 2) = 0$
or $(- 2 + 1)^{5} + [2 \times (- 2) + K]^{3} = 0$
or $- 1 + (K - 4)^{3} = 0$
or $[(K - 4)] = 1$
or $K = 5$

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