Factorise: $4 a^{2} - 4 a - 15$

(2 a - 5) (2 a - 3)

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(2 a - 5) (2 a + 3)

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(2 a + 5) (2 a + 3)

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(5 a - 2) (3 a + 2)

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Solution

The correct option is D $(2 a - 5) (2 a + 3)$
$4 a^{2} - 4 a - 15$
We need to find the two integers whose product is $- 60$ and sum is $- 4$ .
We have, $- 10$ and $6$ as $- 10 \times 6 = - 60$ and $- 10 + 6 = - 4$ .

$∴ 4 a^{2} - 4 a - 15 = 4 a^{2} - 10 a + 6 a - 15$
$= 2 a (2 a - 5) + 3 (2 a - 5)$
$= (2 a - 5) (2 a + 3)$

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