The factors of $(2 x^{2} - 3 x - 2) (2 x^{2} - 3 x) - 63$ are

(x - 3) (2 x + 3) (x - 1) (x - 7)

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(x + 3) (2 x - 3) (x - 1) (x - 7)

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(x + 3) (2 x + 3) (2 x^{2} - 3 x + 7)

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(x - 3) (2 x + 3) (2 x^{2} - 3 x + 7)

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Solution

The correct option is D $(x - 3) (2 x + 3) (2 x^{2} - 3 x + 7)$
Equation is: $(2 x^{2} - 3 x - 2) (2 x^{2} - 3 x) - 63$
Now, let $(2 x^{2} - 3 x)$ = a
The new equation is (a-2)(a) - 63 = $a^{2} - 2 a - 63$
Solving the new equation, we get the factors as: (a-9)(a+7)
Hence, the factors of $(2 x^{2} - 3 x - 2) (2 x^{2} - 3 x) - 63$ = $(2 x^{2} - 3 x - 9) (2 x^{2} - 3 x + 7)$
Factorising it further: $(2 x + 3) (x - 3) (2 x^{2} - 3 x + 7)$

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