X^3+125

. Factor the polynomial completely.

. Set each f the factors equal to 0.

. Solve each of those equation for x

X³ + 125

x³ - 5x² + 5x² + 25x - 25x + 125

x³ - 5x² + 25x + 5x² - 25x + 125

x (x²) - x (5x) + x (25) + 5 (x²) - 5 (5x) + 5 (25)

x (x² - 5x + 25) + 5 (x² - 5x + 25)

(x + 5) (x² - 5x + 25)

f (x) = x³ + 125

f (x) = x³ - 5x² + 5x² + 25x - 25x + 125

f (x) = x³ - 5x² + 25x + 5x² - 25x + 125

f (x) = x (x²) - x (5x) + x (25) + 5 (x²) - 5 (5x) + 5 (25)

f (x) = x (x² - 5x + 25) + 5 (x² - 5x + 25)

f (x) = (x + 5) (x² - 5x + 25)

0 = (x + 5) (x² - 5x + 25)

0 = x + 5 or 0 = x² - 5x + 25

- 5 - 5 x = - (-5) ± √ ((-5) ² - 4 (1) (25))

-5 = x 2 (1)

x = 5 ± √ ((25 - 100)

2

x = 5 ± √ (-75)

2

x = 5 ± 5i√ (3)

2

x = 2.5 ± 2.5i√ (3)

x = 2.5 + 2.5i√ (3) or x = 2.5 - 2.5i√ (3)

Solution Set: {-5, 2.5 ± 2.5i√ (3) }