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If we take a polynomial ($x^4+1$, for instance) I do not see the difference in factoring this polynomial into irreducible polynomials in $\mathbb{C}[x]$ and $\mathbb{R}[x]$. Using this concrete example, can you show this difference?

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    Factor $X^2+1$ into irreducibles in $\mathbb R[X]$ and in $\mathbb C[X]$. Do you see a difference? Once you have done this, do your example.2011-11-28
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    Isn't $x^2+1$ already irreducible?2011-11-28
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    irreducible over what field?2011-11-28

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