document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=362439>Question 362439</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I answer this?  \r<BR>\n" );
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document.write( "Solve the inequality.\r<BR>\n" );
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document.write( "x^4 - 32x^2 - 144 > 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #258299 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=258299\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4+-+32x%5E2+-+144+%3E+0 ALIGN=MIDDLE  ALT=\"x%5E4+-+32x%5E2+-+144+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-36%29%28x%5E2%2B4%29%3E0 ALIGN=MIDDLE  ALT=\"%28x%5E2-36%29%28x%5E2%2B4%29%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-6%29%28x%2B6%29%28x%5E2%2B4%29%3E0 ALIGN=MIDDLE  ALT=\"%28x-6%29%28x%2B6%29%28x%5E2%2B4%29%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Break up the number line into 4 regions using the critical points of the function.<BR>\n" );
document.write( "Region 1:(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity ALIGN=MIDDLE  ALT=\"-infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6 ALIGN=MIDDLE  ALT=\"-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "Region 2:(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6 ALIGN=MIDDLE  ALT=\"-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "Region 3:(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "Region 4:(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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document.write( "For each region, choose a point in the region (not an endpoint).<BR>\n" );
document.write( "Test the inequality.<BR>\n" );
document.write( "If the inequality is satisfied, the region is part of the solution region.<BR>\n" );
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document.write( "Region 1:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-7 ALIGN=MIDDLE  ALT=\"x=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-6%29%28x%2B6%29%28x%5E2%2B4%29%3E0 ALIGN=MIDDLE  ALT=\"%28x-6%29%28x%2B6%29%28x%5E2%2B4%29%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-7-6%29%28-7%2B6%29%28%28-7%29%5E2%2B4%29%3E0 ALIGN=MIDDLE  ALT=\"%28-7-6%29%28-7%2B6%29%28%28-7%29%5E2%2B4%29%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-13%29%28-1%29%2853%29%3E0+ ALIGN=MIDDLE  ALT=\"%28-13%29%28-1%29%2853%29%3E0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=689%3E0+ ALIGN=MIDDLE  ALT=\"689%3E0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "True, Region 1 is part of the solution region.<BR>\n" );
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document.write( "Region 2:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1 ALIGN=MIDDLE  ALT=\"x=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-6%29%28x%2B6%29%28x%5E2%2B4%29%3E0 ALIGN=MIDDLE  ALT=\"%28x-6%29%28x%2B6%29%28x%5E2%2B4%29%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1-6%29%28-1%2B6%29%28%28-1%29%5E2%2B4%29%3E0 ALIGN=MIDDLE  ALT=\"%28-1-6%29%28-1%2B6%29%28%28-1%29%5E2%2B4%29%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-7%29%285%29%285%29%3E0+ ALIGN=MIDDLE  ALT=\"%28-7%29%285%29%285%29%3E0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-175%3E0+ ALIGN=MIDDLE  ALT=\"-175%3E0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "False, Region 2 is part of the solution region.<BR>\n" );
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document.write( "Region 3:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-6%29%28x%2B6%29%28x%5E2%2B4%29%3E0 ALIGN=MIDDLE  ALT=\"%28x-6%29%28x%2B6%29%28x%5E2%2B4%29%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281-6%29%281%2B6%29%28%281%29%5E2%2B4%29%3E0 ALIGN=MIDDLE  ALT=\"%281-6%29%281%2B6%29%28%281%29%5E2%2B4%29%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-5%29%287%29%285%29%3E0+ ALIGN=MIDDLE  ALT=\"%28-5%29%287%29%285%29%3E0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-175%3E0+ ALIGN=MIDDLE  ALT=\"-175%3E0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "False, Region 3 is not part of the solution region.<BR>\n" );
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document.write( "Region 4:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7 ALIGN=MIDDLE  ALT=\"x=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-6%29%28x%2B6%29%28x%5E2%2B4%29%3E0 ALIGN=MIDDLE  ALT=\"%28x-6%29%28x%2B6%29%28x%5E2%2B4%29%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287-6%29%287%2B6%29%28%287%29%5E2%2B4%29%3E0 ALIGN=MIDDLE  ALT=\"%287-6%29%287%2B6%29%28%287%29%5E2%2B4%29%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%29%2813%29%2853%29%3E0+ ALIGN=MIDDLE  ALT=\"%281%29%2813%29%2853%29%3E0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=689%3E0+ ALIGN=MIDDLE  ALT=\"689%3E0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "True, Region 4 is part of the solution region.<BR>\n" );
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document.write( "Solution Region:  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity ALIGN=MIDDLE  ALT=\"-infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6 ALIGN=MIDDLE  ALT=\"-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >) U (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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document.write( "Graphical verification: Look for regions where the function is above the x-axis (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E0 ALIGN=MIDDLE  ALT=\"y%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-10%2C10%2C-600%2C600%2Cgrid%281%29%2Cblue%28line%28-6%2C600%2C-6%2C-600%29%29%2Cblue%28line%286%2C600%2C6%2C-600%29%29%2Cblue%28line%280%2C500%2C0%2C-500%29%29%2Cgraph%28300%2C300%2C-10%2C10%2C-600%2C600%2Cx%5E4+-+32x%5E2+-+144%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );