Question 903024
Break up the number line using the critical points.
{{{x+3=0}}}
{{{x=-3}}}
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{{{x+1=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}}}
{{{(-4+3)^2(-4+1)>0}}}
{{{(-1)^2(-3)>0}}}
{{{-3>0}}}
False, not in the solution region.
Region 2 : {{{x=-2}}}
{{{(-2+3)^2(-2+1)>0}}}
{{{(1)^2(-1)>0}}}
{{{-1>0}}}
False, not in the solution region.
Region 3 : {{{x=0}}}
{{{(0+3)^2(0+1)>0}}}
{{{9>0}}}
True, in the solution region.
So then, the solution region is,
 ({{{-1}}},{{{infinity}}})
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{{{graph(300,300,-5,5,-5,5,(x+3)^2(x+1))}}}