$Factorise: x^{2} + 5 x - 24$

(x + 3) (x + 8)

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(x - 3) (x - 8)

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(x - 3) (x + 8)

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(x + 3) (x - 8)

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Solution

The correct option is C $(x - 3) (x + 8)$
$In order to factorize x^{2} + 5 x - 24, we need to split the middle term 5 x such that the sum or difference is 5 and product is -24.$

$Hence 5x can be written as -3x and 8x.$
$x^{2} - 3 x + 8 x - 24 = x (x - 3) + 8 (x - 3)$

$Taking out (x - 3) common, x^{2} + 5 x - 24 = (x - 3) (x + 8) .$

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