It is a very simple question but I'm stuck in decomposing this: $x^3+2x^2-2$. I can't find the $x-c$ (Ruffini's rule) form that can enable me to decompose it. Is it possible to decompose? If I can solve it, I will be able to resolve an entire math problem!. It is an elementary question I know but I can't find a way to continue after several attemps. Please help me, thanks in advance!
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It's possible to decompose it because it has degree $3$, but the decomposition is awful. If this comes up in an exercise, surely you're not meant to decompose it. – Git Gud Nov 25 '13 at 20:36
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Probably! But I'm curious to find out how it have to be decomposed and however after I decompose it, I'm sure that I can solve the exercise ;-) – Dipok Nov 25 '13 at 20:39
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3Enjoy. – Git Gud Nov 25 '13 at 20:40
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And, what is the exercise you have mentioned ? – Dietrich Burde Nov 25 '13 at 20:52
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calculus of a limit, just solved – Dipok Nov 25 '13 at 20:57
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There probably are easier ways. – Git Gud Nov 25 '13 at 20:58
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I will retry finding easier ways – Dipok Nov 25 '13 at 21:04
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By Eisenstein, the polynomial $x^3 + 2x^2-2$ is $\mathbb Q$-irreducible, so there is no rational number $c$ such that $x-c$ divides your polynomial. It does have a real root $c$, though, which is easiest to find by various approximative processes.
Lubin
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