+128408 x^5-x^4-3x^3+3x^2-4x+4=0
If we can add the coefficients and the result = 0, then 1 is a root
So using synthetic division to find a reduced polynomial, we have
1 [ 1 -1 - 3 +3 -4 4 ]
1 0 -3 0 -4
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1 0 -3 0 -4 0
So.......the remaining polynomial is x^4 - 3x^2 - 4 factor this
(x^2 - 4) (x^2 + 1) =
(x + 2) ( x - 2) (x^2 + 1)
Setting the first two terms to 0 and solving for x we get that x = -2 and x = -2....and these are two other real roots
Finally.........set x^2 + 1 to 0
x^2 + 1 = 0 subtract 1 from both sides
x^2 = -1 and x = i and x = -i are the non-real roots
So the zeroes are -2, 1, 2 , i, -i
