Factorize the below equation:
$x^{2} + 3 x + 2 + a x + 2 a$

(x + 2) (2 x + a + 2)

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(a x - 2) (x + 1)

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(x + 2) (x + a + 1)

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(x - 2) (a + 1)

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Solution

The correct option is C $(x + 2) (x + a + 1)$
$x^{2} + 3 x + 2 + a x + 2 a$
$= (x^{2} + 2 x + x + 2) + a (x + 2)$
$= [x (x + 2) + 1 (x + 2)] + a (x + 2)$
$= (x + 2) (x + a + 1)$

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