Question

How do you factor `x^4-2x^3-12x^2+18x+27`?

Answer 1

Answer `(x+1)(x-3)^2(x+3)`

Try `x=-1` gives `1+2-12-18+27=0` so `x+1` is a factor.
Dividing by `(x+1)` gives `x^3-3x^2-9x+27`
Try `x=3` in cubic gives `27-27-27+27=0` so `x-3` is a factor
Dividing by `(x-3)` gives `x^2-9` which factors to `(x-3)(x+3)`