Factorize the following
$2 a^{2} + 17 a - 30$

(2 a - 3) (a + 10)

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(2 a + 3) (a + 10)

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(2 a - 3) (a - 10)

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None of these

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Solution

The correct option is A $(2 a - 3) (a + 10)$
$2 a^{2} + 17 a - 30$

$20 + - 3 = - 17$ ............the split for the middle term

$20 \times - 3 = - 60$ .............the product of the coefficient of the first and last term

Now splitting the middle term, we get

$= 2 a^{2} + 20 a - 3 a - 30$
$= 2 a (a + 10) - 3 (a + 10)$

$= (a + 10) (2 a - 3)$

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