Question

x^3-x^2-12x>0
Graph the solution set

Answer 1

x^3-x^2-12x>0
x(x^2-x-12)>0
x(x+3)(x-4)>0

Condition 1
x>0
x+3>0
x-4>0
--> x>4 (A)

Condition 2
x<0
x+3<0
x-4>0
--> no answer for x (B)

Condition 3
x<0
x+3>0
x-4<0
--> -3<x<0 (C)

Condition 4
x>0
x+3<0
x-4<0
--> no answer for x (D)

From (A), (B), (C) and (D)
x>4 or -3<x<0