Factorising $X^n+...+X+1$ in $\mathbb{R}$ How can factorize this polynom in $\mathbb{R}$:
$X^n+...+X+1$
I already try to factorize it in $\mathbb{C}$ but I couldn't find a way to turn to $\mathbb{R}$

If you can factor it in $\mathbb{C}$ you already have factored it in $\mathbb{R}$ - just multiply each pair of complex monoids by each other, since each complex root has a conjugate root as well.
Since your roots are $(-1)^{k/(n+1)}$, and $(-1)^{k/(n+1)}+(-1)^{(n+1-k)/(n+1)}\in\mathbb{R}$, you should be able to factor out your polynomial.
If $n$ is even, you have $n/2$ quadric factors. When $n$ is odd, the factor $(x+1)$ is added.
