Factorise the following:
$3 (x^{2} - 5 x)^{2} - 2 (x^{2} - 5 x + 5) - 6$

(x^{2} - 5 x + 2) (3 x^{2} - 5 x - 8)

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(x^{2} - 5 x + 2) (3 x^{2} - 15 x - 8)

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(x^{2} - 5 x - 2) (3 x^{2} - 15 x + 8)

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(x^{2} - 5 x - 2) (3 x^{2} - 5 x + 8)

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Solution

The correct option is B $(x^{2} - 5 x + 2) (3 x^{2} - 15 x - 8)$
$3 (x^{2} - 5 x)^{2} - 2 (x^{2} - 5 x + 5) - 6$
Let, $(x^{2} - 5 x)$ be $a$
$3 (a)^{2} - 2 (a + 5) - 6$
$= 3 a^{2} - 2 a - 10 - 6$
$= 3 a^{2} - 2 a - 16$
$= 3 a^{2} + 6 a - 8 a - 16$
$= 3 a (a + 2) - 8 (a + 2)$
$= (a + 2) (3 a - 8)$
Resubstituting the value of $a$ we get,
$(x^{2} - 5 x + 2) [3 (x^{2} - 5 x) - 8)]$
$= (x^{2} - 5 x + 2) (3 x^{2} - 15 x - 8)$

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