document.write( "Question 958643: What are the Interval Notation of -45-21x+x^2+x^3 ≥0
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Algebra.Com's Answer #585989 by Fombitz(32388) $\"\"$ $\"About$

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$\"-45-21x%2Bx%5E2%2Bx%5E3%3E=0\"$
\n" ); document.write( " $\"%28x-5%29%28x%2B3%29%5E2%3E=0\"$
\n" ); document.write( "Break up the number line using the critical points of the left hand side.
\n" ); document.write( " $\"x=5\"$ and $\"x=-3\"$
\n" ); document.write( "Region 1 : $\"x%3C-3\"$
\n" ); document.write( "Region 2 : $\"-3%3Cx%3C5\"$
\n" ); document.write( "Region 3 : $\"x%3E5\"$
\n" ); document.write( "Choose a point in each region, test the inequality.
\n" ); document.write( "Region 1 : $\"x=-4\"$
\n" ); document.write( " $\"%28-4-5%29%28-4%2B3%29%5E2%3E0\"$
\n" ); document.write( " $\"%28-9%29%28-1%29%5E2%3E0\"$
\n" ); document.write( " $\"-9%3E0\"$
\n" ); document.write( "False, so region 1 is not part of the solution region.
\n" ); document.write( "Region 2 : $\"x=0\"$
\n" ); document.write( " $\"%280-5%29%280%2B3%29%5E2%3E0\"$
\n" ); document.write( " $\"%28-5%299%3E0\"$
\n" ); document.write( " $\"-45%3E0\"$
\n" ); document.write( "False, so region 2 is not part of the solution region.
\n" ); document.write( "Region 3 : $\"x=6\"$
\n" ); document.write( " $\"%286-5%29%286%2B3%29%5E2%3E0\"$
\n" ); document.write( " $\"%281%2981%3E0\"$
\n" ); document.write( " $\"81%3E0\"$
\n" ); document.write( "True, so region 3 is part of the solution region.
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\n" ); document.write( " $\"x%3E=5\"$
\n" ); document.write( "In interval notation,
\n" ); document.write( "[ $\"5\"$ , $\"infinity\"$ )\r
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