Factorize :
$(a^{3} - 3 a) (a^{2} - 3 a + 7) + 10$

(a^{2} - a + 5) (a + 2) (a + 1)

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(a^{3} - 3 a + 5) (a + 2) (a - 1)

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(a^{2} - 3 a + 5) (a - 2) (a - 1)

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(a^{3} - 3 a + 5) (a - 2) (a + 1)

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Solution

The correct option is C $(a^{2} - 3 a + 5) (a - 2) (a - 1)$
$(a^{3} - 3 a) (a^{2} - 3 a + 7) + 10$
Let $a^{2} - 3 a = a$
$=> (a) (a + 7) + 10$
$=> a^{2} + 7 a + 10$
$=> a^{2} + 5 a + 2 a + 10$
$=> a (a + 5) + 2 (a + 5)$
$=> (a + 5) (a + 2)$
Putting the value of $a$
$=> (a^{2} - 3 a + 5) (a^{2} - 3 a + 2)$
$=> (a^{2} - 3 a + 5) (a^{2} - 2 a - a + 2)$
$=> (a^{2} - 3 a + 5) [(a (a - 2) - 1 (a - 2)]$
$=> (a^{2} - 3 a + 5) (a - 2) (a - 1)$

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