document.write( "Question 339897: How do i solve this polynomial inequality?\r
\n" ); document.write( "\n" ); document.write( "x^3+2x^2-3x>0. \n" ); document.write( "

Algebra.Com's Answer #243560 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
First factor,
\n" ); document.write( " $\"x%5E3%2B2x%5E2-3x%3E0\"$
\n" ); document.write( " $\"x%28x%5E2%2B2x-3%29%3E0\"$
\n" ); document.write( " $\"x%28x%2B3%29%28x-1%29%3E0\"$
\n" ); document.write( "Now break up the number line into 4 regions base on the zeros of the polynomial,
\n" ); document.write( "Region 1: ( $\"-infinity\"$ , $\"-3\"$ )
\n" ); document.write( "Region 2: ( $\"-3\"$ , $\"0\"$ )
\n" ); document.write( "Region 3: ( $\"0\"$ , $\"1\"$ )
\n" ); document.write( "Region 4: ( $\"1\"$ , $\"-infinity\"$ )
\n" ); document.write( "For each region choose a point in the region (not an endpoint).
\n" ); document.write( "Test the inequality.
\n" ); document.write( "If the inequality is satsfied, that region is part of the solution region.
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\n" ); document.write( "Region 1: $\"x=-4\"$
\n" ); document.write( " $\"x%28x%2B3%29%28x-1%29%3E0\"$
\n" ); document.write( " $\"-4%28-4%2B3%29%28-4-1%29%3E0\"$
\n" ); document.write( " $\"-4%28-1%29%28-5%29%3E0\"$
\n" ); document.write( " $\"-20%3E0\"$
\n" ); document.write( "False, this region is not part of the solution region.
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\n" ); document.write( "Region 2: $\"x=-2\"$
\n" ); document.write( " $\"x%28x%2B3%29%28x-1%29%3E0\"$
\n" ); document.write( " $\"-2%28-2%2B3%29%28-2-1%29%3E0\"$
\n" ); document.write( " $\"-2%281%29%28-3%29%3E0\"$
\n" ); document.write( " $\"6%3E0\"$
\n" ); document.write( "True, this region is part of the solution region.
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\n" ); document.write( "Region 3: $\"x=1%2F2\"$
\n" ); document.write( " $\"x%28x%2B3%29%28x-1%29%3E0\"$
\n" ); document.write( " $\"%281%2F2%29%281%2F2%2B3%29%281%2F2-1%29%3E0\"$
\n" ); document.write( " $\"1%2F2%287%2F2%29%28-1%2F2%29%3E0\"$
\n" ); document.write( " $\"-7%2F8%3E0\"$
\n" ); document.write( "False, this region is not part of the solution region.
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\n" ); document.write( "Region 4: $\"x=2\"$
\n" ); document.write( " $\"x%28x%2B3%29%28x-1%29%3E0\"$
\n" ); document.write( " $\"2%282%2B3%29%282-1%29%3E0\"$
\n" ); document.write( " $\"2%285%29%281%29%3E0\"$
\n" ); document.write( " $\"10%3E0\"$
\n" ); document.write( "True, this region is part of the solution region.
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\n" ); document.write( "Solution Region :( $\"-3\"$ , $\"0\"$ ) U ( $\"1\"$ , $\"-infinity\"$ )
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\n" ); document.write( "Graphical verification: Look for the region where the function is above the x-axis.
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