## PhoenixFire 3 years ago Factoring a cubic polynomial. $x^3-108x^2+3564x-34992$ I haven't needed to factor a cubic in a while and have forgotten how. Any help? I know the answers, just can't get them.

1. anonymous

I know how to factor, but explaining it to someone is complicated. I haven't factored in so long either. I'll try to explain it. Sorry if I'm no help.. :/

3. anonymous

Sorry I can't help you. >_< I'm a failed Amby on my first day. :c

4. anonymous

$\begin{array}{l} {x^3} - 108{x^2} + 3564x - 34992 \\ = x({x^2} - 108x + 2916) + 648(x - 54) \\ = x{(x - 54)^2} + 648(x - 54) \\ = (x - 54)({x^2} - 54x + 648) \\ = (x - 54)(x - 36)(x - 18) \\ \end{array}$

5. anonymous

@drawar from where did you 2916?

6. anonymous

54^2

7. anonymous

8. anonymous

Yes but you have to bring it in, and subtract it later, that's the one and only trick when doing factorization of polynomials.

9. anonymous

Where did you subtract it? And in which course did you take this?

10. anonymous

3564=2916+648

11. anonymous

I don't remember which course, I think it's common sense, no?

12. anonymous

Can you please explain the before the last step? I don't get it, how did you reach to that point?

13. anonymous

@drawar

14. anonymous

Use a calculator to get 2 roots