Verified answer

x⁴ + 4 = (x⁴ + 4x² + 4) - 4x² = (x² + 2)² - 4x² = (x² + 2)² - (2x)² =

= (x² + 2 - 2x)(x² + 2 + 2x) = (x² - 2x + 2)(x² + 2x + 2)