Factorise $p(z)=z^5-5z^4+10z^3-10z^2-11z+15$ given that $z=1-2i$ is a root and that three roots are integers.(mobius)

 

This is the factorisation of $p(z)$ into real linear factors and real quadratic factors.

ANSWER: The answer to the original question is that the complex linear factors of $p(z)$ are $$(z-1),(z+1),(z-3),(z-1+2i)(z-1-2i)\ .$$