SOLUTION: What are the Interval Notation of -45-21x+x^2+x^3 ≥0

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Question 958643: What are the Interval Notation of -45-21x+x^2+x^3 ≥0
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
-45-21x%2Bx%5E2%2Bx%5E3%3E=0
%28x-5%29%28x%2B3%29%5E2%3E=0
Break up the number line using the critical points of the left hand side.
x=5 and x=-3
Region 1 : x%3C-3
Region 2 : -3%3Cx%3C5
Region 3 : x%3E5
Choose a point in each region, test the inequality.
Region 1 : x=-4
%28-4-5%29%28-4%2B3%29%5E2%3E0
%28-9%29%28-1%29%5E2%3E0
-9%3E0
False, so region 1 is not part of the solution region.
Region 2 : x=0
%280-5%29%280%2B3%29%5E2%3E0
%28-5%299%3E0
-45%3E0
False, so region 2 is not part of the solution region.
Region 3 : x=6
%286-5%29%286%2B3%29%5E2%3E0
%281%2981%3E0
81%3E0
True, so region 3 is part of the solution region.
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x%3E=5
In interval notation,
[5,infinity)