$$
x^{28}+9x^{26}+39x^{24}+95x^{22}+76x^{20}-384x^{18}-1928x^{16}-4868x^{14}-7712x^{12}-6144x^{10}+4864x^{8}+24320x^{6}+39936x^{4}+36864x^{2}+16384
$$

In an [example](https://math.stackexchange.com/q/3316008/19341) the polynomial above arose. It should have six factors, each like 
$$
(x^4-4x^2\cos(4\pi c\_\color{blue}{\text{r}}) +4)
$$
and one like $$
(x^4-4x^2\cosh(4\pi c\_\color{red}{\text{n}})+4).
$$
to match the degree $6\cdot4+4=28$ of the first.

Is it possible to first do the polynomial division and then determine the values of $\cos(4\pi c)$?

Or the other way: Why not just multiplying all the factors to get a set of equation? These are elementary symmetric polynomials in the variables $\cos(h)(4\pi c\_{r/n})$ with integer solutions. 

> 
> Is this approach known to work for a class of cases? What can we say about the angles $\cos(h)(4\pi c\_{r/n})$ because of that elementary symmetric polynomial integer solution contraint?
> 
> 
>