Solve: (x-2)^3(x+5)^2<0 ?
Answer:
Once again, you set the expression =0 to find critical points then test the regions.
(x-2}³(x+5)² = 0
It doesn’t matter that each factor is raised to a power, because when each = 0, the products will be =0.
So, x=2 or x= -5
Testing the regions, we’ll try -10, 10 and 0
[(-10)-2]³[(-10)+5]² = (-12)³(-5)² = -1728*25 which is <0
[(10)-2]³[(10)+5]² = (8)³(15)² which is NOT <0
[(0)-2]³[(0)+5]² = (-2)³(5)² = -8*25 which is <0
So we know that x< -5 or -5 <x<2
We can’t combine them into one statement, because x≠ -5
so the solution is
x< -5 or -5 <x<2
