How do you solve #x (x^2 + 2x + 3)=4# by factoring?
First multiply out and write in standard polynomial form to obtain
This is now a 3rd degree cubic equation and has 3 roots.
We may use the remainder theorem, which involves first obtaining a single root by inspection, and then long dividing the corresponding factor into the cubic and then factorizing the resultant quadratic by factors.
Now if we let
Starting with initial value
Now since this is not an integer value, we cannot long divide
So the best way will be to continue using Newton's method for the other 2 roots as well, and then rewrite the original polynomial in factor form like that.
I leave the details as an exercise :)