Answer: x = {-5, -1, 0, 1}
Step-by-step explanation:
f(x) = x⁴ + 5x³ - x² - 5x
0 = x⁴ + 5x³ - x² - 5x
= x(x³ + 5x² - x - 5)
= ↓ x²(x + 5) -1(x + 5)
= ↓ (x + 5)(x²- 1)
= ↓ ↓ (x + 1)(x - 1)
0 = x(x + 5)(x + 1)(x - 1)
x = 0 ⇒ x = 0
x + 5 = 0 ⇒ x = -5
x + 1 = 0 ⇒ x = -1
x - 1 = 0 ⇒ x = 1
