How do I Factor Odd and even Degree polynomial as a product of irreducible polynomial? I want to factor $x^n -1$ Into a product of irreducible polynomials over The Reals, when n is Odd and when n is even. 
I know that The only irreducible polynomials over The Real are first Degree and second Degree polynomials. 
But im stuck, so any hints would be great 

The linear factors are easy because the real roots of $x^n -1$ can only be $\pm 1$.
Irreducible quadratic factors come from complex roots.
The complex roots of $x^n -1$ are the $n$-th roots of unit: $\omega^k$, where $\omega=\exp(\frac{2\pi}{n} i)$.
These roots come in conjugate pairs: $\omega^k, \bar\omega = \omega^{n-k}$. The quadratic polynomial having them as roots has real coefficients and is irreducible.
Full solution:
Linear factors:

 When $n$ is odd, the only linear factor of  $x^n -1$ is $x-1$.

and

 When $n$ is even, the only linear factors of $x^n -1$ are $(x-1)(x+1)$.

Quadratic factors:

 The quadratic factors of $x^n -1$ are $x^2-2Re(\omega^k)+1$ for $k=2,\dots,n-1$.

