$2+i$ is given to be one of the roots of the polynomial.
I am doing this as a practice for exam prep.
Since $2+i$, is a root, then $(z-2-i)$ is a factor?
So I have:
$(z-2-i)(z^3-Az^2-Bz+C) = z^4-2z^3-z^2+2z+10$
Then, I group the $z$ terms of the same degrees after I multiply out?
Am I on the right track? Because it seems like this will take quite a while in exam conditions? Thanks for any direction!