-x³ - 4x + x^4 + 2x² - 8 = 0
-x(x² + 4) + (x² - 2)(x² + 4) = 0
(x² + 4)(x² - 2 - x) = 0
(x² + 4)(x² - x - 2) = 0
(x² + 4)(x - 2)(x + 1) = 0

Finally, by zero-product property:

x² + 4 = 0 and x - 2 = 0 and x + 1 = 0
x² = -4 and x = {2,-1}
x = ±v-4 and x = {-1,2}
x = {-1, 2, ±2i}

I hope this helps!

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