Factors of the $$(2x^2 - 3x -2)(2x^2 - 3x) - 63$$ , is​

Correct option is D

Given:

(2x^2 - 3x - 2)(2x^2 - 3x) - 63

Solution:

Let:

A = $$2x^2 - 3x$$​​

Then the expression becomes:

​$$(A - 2)(A) - 63 = A^2 - 2A - 63$$​​

Now factor the quadratic:

​$$A^2 - 2A - 63 = (A - 9)(A + 7)$$​​

Now, substitute $$A = 2x^2 - 3x:$$​​

​$$(A - 9)(A + 7) = (2x^2 - 3x - 9)(2x^2 - 3x + 7) \\ \ \\ =(2x^2 - 6x+3x - 9)(2x^2 - 3x + 7)\\ \ \\ = [2x(x - 3+3(x - 3)](2x^2 - 3x + 7)\\ \ \\ = (2x+3)(x-3)(2x^2 - 3x + 7)$$​​