SOLUTION: (x+3)^2(x+1)>0

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Question 903024: (x+3)^2(x+1)>0
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Break up the number line using the critical points.
x%2B3=0
x=-3
.
.
.
x%2B1=0
x=-1
So the three regions are:
Region 1: (-infinity,-3)
Region 2: (-3,-1)
Region 3: (-1,infinity)
Choose a point in each region (not an engpoint) and test the inequality.
If the inequality is satisfied, the region is part of the solution.
Region 1 : x=-4
%28-4%2B3%29%5E2%28-4%2B1%29%3E0
%28-1%29%5E2%28-3%29%3E0
-3%3E0
False, not in the solution region.
Region 2 : x=-2
%28-2%2B3%29%5E2%28-2%2B1%29%3E0
%281%29%5E2%28-1%29%3E0
-1%3E0
False, not in the solution region.
Region 3 : x=0
%280%2B3%29%5E2%280%2B1%29%3E0
9%3E0
True, in the solution region.
So then, the solution region is,
(-1,infinity)
.
.
.
graph%28300%2C300%2C-5%2C5%2C-5%2C5%2C%28x%2B3%29%5E2%28x%2B1%29%29