Question 958643
{{{-45-21x+x^2+x^3>=0}}}
{{{(x-5)(x+3)^2>=0}}}
Break up the number line using the critical points of the left hand side.
{{{x=5}}} and {{{x=-3}}}
Region 1 : {{{x<-3}}}
Region 2 : {{{-3<x<5}}}
Region 3 : {{{x>5}}}
Choose a point in each region, test the inequality.
Region 1 : {{{x=-4}}}
{{{(-4-5)(-4+3)^2>0}}}
{{{(-9)(-1)^2>0}}}
{{{-9>0}}}
False, so region 1 is not part of the solution region.
Region 2 : {{{x=0}}}
{{{(0-5)(0+3)^2>0}}}
{{{(-5)9>0}}}
{{{-45>0}}}
False, so region 2 is not part of the solution region.
Region 3 : {{{x=6}}}
{{{(6-5)(6+3)^2>0}}}
{{{(1)81>0}}}
{{{81>0}}}
True, so region 3 is part of the solution region.
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{{{x>=5}}}
In interval notation,
[{{{5}}},{{{infinity}}})