document.write( "Question 903024: (x+3)^2(x+1)>0 \n" ); document.write( "

Algebra.Com's Answer #547769 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
Break up the number line using the critical points.
\n" ); document.write( " $\"x%2B3=0\"$
\n" ); document.write( " $\"x=-3\"$
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\n" ); document.write( " $\"x%2B1=0\"$
\n" ); document.write( " $\"x=-1\"$
\n" ); document.write( "So the three regions are:
\n" ); document.write( "Region 1: ( $\"-infinity\"$ , $\"-3\"$ )
\n" ); document.write( "Region 2: ( $\"-3\"$ , $\"-1\"$ )
\n" ); document.write( "Region 3: ( $\"-1\"$ , $\"infinity\"$ )
\n" ); document.write( "Choose a point in each region (not an engpoint) and test the inequality.
\n" ); document.write( "If the inequality is satisfied, the region is part of the solution.
\n" ); document.write( "Region 1 : $\"x=-4\"$
\n" ); document.write( " $\"%28-4%2B3%29%5E2%28-4%2B1%29%3E0\"$
\n" ); document.write( " $\"%28-1%29%5E2%28-3%29%3E0\"$
\n" ); document.write( " $\"-3%3E0\"$
\n" ); document.write( "False, not in the solution region.
\n" ); document.write( "Region 2 : $\"x=-2\"$
\n" ); document.write( " $\"%28-2%2B3%29%5E2%28-2%2B1%29%3E0\"$
\n" ); document.write( " $\"%281%29%5E2%28-1%29%3E0\"$
\n" ); document.write( " $\"-1%3E0\"$
\n" ); document.write( "False, not in the solution region.
\n" ); document.write( "Region 3 : $\"x=0\"$
\n" ); document.write( " $\"%280%2B3%29%5E2%280%2B1%29%3E0\"$
\n" ); document.write( " $\"9%3E0\"$
\n" ); document.write( "True, in the solution region.
\n" ); document.write( "So then, the solution region is,
\n" ); document.write( " ( $\"-1\"$ , $\"infinity\"$ )
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\n" ); document.write( " $\"graph%28300%2C300%2C-5%2C5%2C-5%2C5%2C%28x%2B3%29%5E2%28x%2B1%29%29\"$
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