How do you factor (2x - 3)^3 - 27?

1 Answer
May 9, 2015

Factoring (2x-3)^3 -27

Consider a related problem:
Find the solutions for (2x-3)^3 -27 = 0

(2x-3)^3 = 27

(2x-3)^3 = 3^3

2x-3 = 3

x=3

So (x-3) is a factor of (2x-3)^3-27

Using synthetic division we can determine that
(2x-3)^3-27 = (x-3)(8x^2-12x+18)

We can extract a common factor of (2) from this final factor
(2x-3)^3-27 = (x-3)(2)(4x^2-6x+9)

Examining the discriminant of (4x^2-6x+9) reveals that there are no further factors.