I just have one simple question about the basics of factoring.

Lets say we have 4x^3 - 24x^2 - 3x + 18

= (4x^3 - 24x^2) + (-3x + 18)

= 4x^2(x - 6) -3(x - 6) I get this part where you're factoring out common factors

This is where I get confused.... the book says the answer is

(4x^2 - 3) (x - 6)

It doesn't say anything on how it got the answer so I'm kinda stumped on what to do.

Any help would be appreciated.

Thanks!