x^3 - 5x^2 +8x-4=0 Answer is 1 or 2 but having difficulty figuring out how to solve this other than trial and error.

We could use DesCartes rule of signs, to show 3 positive roots, then the rational zeros test to narrow the choices. Finally using synthetic division to get them. However, since we know them and they are rational, let's factor.


Then...