If the HCF of $x^{2} - x - 6 a n d x^{2} + 9 x + 14$ is (x + m), then the value of m is

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Solution

The correct option is B 2
$x^{2} - x - 6$
$\Rightarrow x^{2} - 3 x + 2 x - 6$
$\Rightarrow x (x - 3) + 2 (x - 3)$
$\Rightarrow (x - 3) (x + 2)$
$x^{2} + 9 x + 14$
$\Rightarrow x^{2} + 7 x + 2 x + 14$
$\Rightarrow x (x + 7) + 2 (x + 7)$
$\Rightarrow (x + 7) (x + 2)$
So HCF= $(x + 2)$
Hence m=2

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