Factorize the following
$2 x^{2} - 3 x - 14$

(x + 2) (2 x - 7)

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(x - 2) (2 x - 7)

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(x + 2) (2 x + 7)

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None of these

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Solution

The correct option is B $(x + 2) (2 x - 7)$
$2 x^{2} - 3 x - 14$

$- 7 + 4 = - 3$ ...........the split for the middle term

$- 7 \times 4 = - 28$ .............the product of the coefficient of the first and last term

Now, splitting the middle term we get

$= 2 x^{2} + 4 x - 7 x - 14$

$= 2 x (x + 2) - 7 (x + 2)$

$= (x + 2) (2 x - 7)$

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