Complex quartic factorisation

Question

Answer: I'm really not sure how to factorise. I understand that z.z* gives 2Re(z) but it's still not clear to me how it works.

Answer 1

Hint:

$$\dfrac{w^5+1}{w+1}=?$$

For $c,$ use Quadratic substitution question: applying substitution $p=x+\frac1x$ to $2x^4+x^3-6x^2+x+2=0$