Procedure Solve the inequality: (x -3)(x+1)>0 That happens in two cases.
1) When both factors >0 x-3>0 and x+1>0 x>3 and x >-1
The intersection is x >3
2) When both factors <0 x-3<0 and x+1<0 x<3 and x<-1
the intersection is x<-1.
We have obtained that the function is positive for the intervals x < -1 and x > 3. But in one of those intervals the function is decresing and in the other is increasing.
You can recognize that the function given is a parabola and, because the coefficient of the quadratic term is positive, the parabola opens upward. Then the function is decreasing in the first interval and increasing in the second interval.
