Question

X^3+125

.Factor the polynomial completely.
.Set each f the factors equal to 0.
.Solve each of those equation for x

Answer 1

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)}