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## PhoenixFire 2 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.

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1. Kitt020912

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.. :/

2. maddyx

http://answers.yahoo.com/question/index?qid=20080417160912AAt8IHC This could help :)

3. Kitt020912

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

4. drawar

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

5. Boblovesmath

@drawar from where did you 2916?

6. drawar

54^2

7. Boblovesmath

I know but it is not found in the original equation.

8. drawar

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. Boblovesmath

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

10. drawar

3564=2916+648

11. drawar

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

12. Boblovesmath

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

13. Boblovesmath

@drawar

14. drawar

Use a calculator to get 2 roots

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