Final answer:
The binomial that is a factor of x⁴ - 4x² - 4x + 8 is (x - 2).
Step-by-step explanation:
The binomial that is a factor of x⁴ - 4x² - 4x + 8 is (x - 2).
To find the factor, we can use polynomial long division or synthetic division. When we divide x⁴ - 4x² - 4x + 8 by (x - 2), the remainder is 0, indicating that (x - 2) is indeed a factor.