X⁵ + 3x⁴ - 5x³ - 15x² + 4x + 12 = 0
x⁴(x + 3) - 5x²(x + 3) + 4(x + 3) = 0
(x + 3)(x⁴ - 5x² + 4) = 0
1) x + 3 = 0
x = -3
2) x⁴ - 5x² + 4 = 0
t = x², t ≥ 0
t² - 5t + 4 = 0
t₁ + t₂ = 5
t₁t₂ = 4
t₁ = 1; t₂ = 4
Обратная замена:
x² = 1 ⇒ x = -1; 1
x² = 4 ⇒ x = -2; 2
Ответ: x = -3; -2; -1; 1; 2.