The highest common factor of the expressions $x^{2} + x - (K + 7)$ and $2 x^{2} + K x - 12$ is $x + 4$ , the value of $K$ will be

- 5

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- 4

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0

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5

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Solution

The correct option is D $5$
$∵ x + 4 = 0$
$\Rightarrow x = - 4$
$∴$ On putting $x = - 4$ in each of the expression the remainder will be zero
$\Rightarrow (- 4)^{2} + (- 4) - (k + 7) = 0$
$\Rightarrow 16 - 4 - k - 7 = 0$
$∴ k = 5$
Or $2 x^{2} + k x - 12$
$∵ x + 4 = 0$
$\Rightarrow x = - 4$
$∴$ On putting $x = - 4$ in each of the expression the remainder will be zero
$2 (4)^{2} + k (4) - 12 = 0$
$\Rightarrow 32 + 4 k - 12 = 0$
$\Rightarrow 4 k = 20$
$\Rightarrow k = 5$

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