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 $(x - 3) (2 x + 3) (2 x^{2} - 3 x + 7)$
Consider the given expression.
$(2 x^{2} - 3 x - 2) (2 x^{2} - 3 x) - 63$
$\Rightarrow 4 x^{4} - 12 x^{3} + 5 x^{2} + 6 x - 63$
$\Rightarrow 4 x^{3} (x - 3) + (x - 3) (5 x + 21)$
$\Rightarrow (x - 3) (4 x^{3} + 5 x + 21)$
$\Rightarrow (x - 3) (4 x^{3} - 6 x^{2} + 6 x^{2} + 5 x + 21)$
$\Rightarrow (x - 3) (4 x^{3} - 6 x^{2} + 6 x^{2} + 14 x - 9 x + 21)$
$\Rightarrow (x - 3) (4 x^{3} - 6 x^{2} + 14 x + 6 x^{2} - 9 x + 21)$
$\Rightarrow (x - 3) (2 x + 3) (2 x^{2} - 3 x + 7)$

Hence, this is the answer.

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