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?
Difference between factoring into irreducibles in $\mathbb{C}[x]$ and $\mathbb{R}[x]$?
0
$\begingroup$
polynomials
-
2Factor $X^2+1$ 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
-
0Isn't $x^2+1$ already irreducible? – 2011-11-28
-
3irreducible over what field? – 2011-11-28