Network function. 6th degree polynomial to complex numbers

[nearxos]

Homework Statement

the problem that i attached bellow is related to how you can obtain a transfer function from its squared magnituded.

my question is not on the problem it self as its just a solved example from my book.
what i find difficult to understand as you can see from my attachment is how the 6th degree polynomial was break down to equations that involves complex number.

 

[danago]

You could easily find the six zeros of the polynomial in the denominator using software such as MATLAB and then write it as a product of its factors, given that (s-k) is a factor of a polynomial f(s) if and only if f(k)=0

 

[nearxos]

I know how to solve it with matlab. But I need to know how I can do it on paper.

Thanks for the reply