I would have done the same thing synthetic division or long divison. I would try the multiples of
8 = 1, 2, 4, 8 plus or minus versions.
try (x+2)
2 | 1 -1 -6 4 8
| 2 2 -8 -8
------------------------------------
1 1 -4 -4 0
so (x + 2)(x^3 - 4x^2 - 4x)
factor out an x
x(x + 2)(x^2 - 4x - 4)
x(x + 2)(x +2)(x - 2) set = 0
x = 0 or x = -2 or x = 2
-1 is not a root 0 is...