What is the completely factored form of 40x^3 - 60x^2 - 10x + 15?

To find the completely factored form of the expression 40x^3 - 60x^2 - 10x + 15, we can start by factoring by grouping.

First, combine the terms in pairs:

1. From the first pair, 40x^3 and -60x^2, we can factor out 20x^2, yielding:

20x^2(2x - 3).

2. For the second pair, -10x and +15, we can factor out -5, resulting in:

-5(2x - 3).

Now we have:

20x^2(2x - 3) - 5(2x - 3).

Next, we can factor out the common binomial (2x - 3):

(2x - 3)(20x^2 - 5).

Now, observe that the expression 20x^2 - 5 can be factored further. Factoring out a 5 gives:

5(4x^2 - 1).

Recognizing 4x^2 - 1 as a difference of squares, we can factor it into (2x - 1)(2