2x4-2x3-2x2-2x-4=2(x4-x3-x2-x-2).
By inspection, x=-1 is a zero: 2(1+1-1+1-2)=0.
Divide by this zero:
-1 | 1 -1 -1 -1 -2
1 -1 2 -1 | 2
1 -2 1 -2 | 0 = x3-2x2+x-2=x(x2+1)-2(x2+1)=(x-2)(x2+1).
So the remaining zeroes are 2, i, -i.
Zeroes are -1, 2, i, -i.