Factorize :
$(a^{2} - a) (4 a^{2} - 4 a - 5) - 6$

(a + 2) (a + 1) (4 a^{2} - 4 a + 3)

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(a - 2) (a - 1) (4 a^{2} - 4 a + 3)

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(a - 2) (a + 1) (4 a^{2} + 4 a + 3)

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(a - 2) (a + 1) (4 a^{2} - 4 a + 3)

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Solution

The correct option is D $(a - 2) (a + 1) (4 a^{2} - 4 a + 3)$
$(a^{2} - a) (4 a^{2} - 4 a - 5) - 6$
$= (a^{2} - a) [4 (a^{2} - a) - 5] - 6$
Let $(a^{2} - a) = x$
Thus,
$x (4 x - 5) - 6$
$= 4 x^{2} - 5 x - 6$
$= 4 x^{2} - 8 x + 3 x - 6$
$= 4 x (x - 2) + 3 (x - 2)$
$= (x - 2) (4 x + 3)$
Putting the value of $x$
$= (a^{2} - a - 2) [4 (a^{2} - a) + 3]$
$= (a^{2} - 2 a + a - 2) (4 a^{2} - 4 a + 3)$
$= (a (a - 2) + 1 (a - 2)) (4 a^{2} - 4 a + 3)$
$= (a - 2) (a + 1) (4 a^{2} - 4 a + 3)$

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