Question

How do you get from x^4-6x^2+8 to (x^2-2)(x-2)(x+2)? Is there a formula?

Answer 1

You need to factor. When you look at x^4 - 6x^2 + 8, you may notice that if you substitute u for x^2, by letting u = x^2, then u^2 = x^4. Then you have:
u^2 - 6u + 8
Now this looks like a simple 2nd degree polynomial that should be easy to factor:
(u - 4)(u - 2)
Do you follow so far?

Answer 2

Once you have
(u - 4)(u - 2), substitute back x^2 = u
(x^2 - 4)(x^2 - 2)
The left factor is the diference of two squares, so we can factor it:
(x+ 2)(x - 2)(x^2 - 2)

Answer 3

OMG, I can't believe I didn't get this on my own. Thanks for your help mathstudent55, I should of figured it is something simple like this.