Question

Factor the polynomial function f(x). Then solve equation f(x)= 0. f(x)= x^3 +5x^2 -2x-24.

Answer 1

f(x) = x^3 + 5x^2 - 2x - 24
0 = x^3 + 5x^2 - 2x - 24
0 = x^2(x + 5) - 2(x + 12)
0 = x^2(x + 5) - 4(x + 12) + 2(x + 12)
0 = x^2(x + 5) - 4(x + 5 + 7) + 2(x + 12)
0 = x^2(x + 5) -4(x + 5) - 28 + 2(x + 12)
0 = (x + 5)(x^2 - 4) - 28 + 2(x + 12)
0 = (x + 5)(x + 2)(x - 2) - 28 + 2x + 24
0 = (x + 5)(x + 2)(x - 2) + 2x - 4
0 = (x + 5)(x + 2)(x - 2) + 2(x - 2)
0 = (x - 2)((x + 5)(x + 2) + 2)
0 = (x - 2)(x^2 + 7x + 10 + 2)
0 = (x - 2)(x^2 + 7x + 12)
0 = (x - 2)((x +3)(x + 4))
0 = (x - 2)(x + 3)(x + 4)

x - 2 = 0
x + 3 = 0
x + 4 = 0

x = 2
x = -3
x = -4

Answer 2

@Bree2012, good luck understanding the steps. If you have any questions, feel free to ask.