document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=467415>Question 467415</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could you please help me with this? I have a huge final this week. I believe the answer is they are all real numbers. Am I correct? Thanks for all your help!!\r<BR>\n" );
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document.write( "(x+8)(x-13)(x+3)>0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #320714 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=320714\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, find the zeros of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x%2B8%29%28x-13%29%28x%2B3%29 ALIGN=MIDDLE  ALT=\"y=%28x%2B8%29%28x-13%29%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "(x+8)(x-13)(x+3)=0\r<BR>\n" );
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document.write( "x+8=0 or x-13=0 or x+3=0\r<BR>\n" );
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document.write( "x=-8, x=13, or x=-3\r<BR>\n" );
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document.write( "In ascending order, the zeros are: -8,-3,13\r<BR>\n" );
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document.write( "Now in the interval <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(-\infty,-8\right)\">, (x+8)(x-13)(x+3) is negative. Simply plug in any negative number less than -8 to see this (eg: plug in x=-10 to get (-10+8)(-10-13)(-10+3)=-322)\r<BR>\n" );
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document.write( "In the interval <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(-8,-3\right)\">, (x+8)(x-13)(x+3) is positive. Simply plug in any number in the interval to see this (eg: plug in x=-5 to get (-5+8)(-5-13)(-5+3)=108) \r<BR>\n" );
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document.write( "In the interval <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(-3,13\right)\">, (x+8)(x-13)(x+3) is negative. Simply plug in any number in the interval to see this (eg: plug in x=0 to get (0+8)(0-13)(0+3)=-312) \r<BR>\n" );
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document.write( "Finally, in the interval <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(13,\infty\right)\">, (x+8)(x-13)(x+3) is positive. Simply plug in any number greater than 13 to see this (eg: plug in x=50 to get (50+8)(50-13)(50+3)=113738) \r<BR>\n" );
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document.write( "So the following intervals make (x+8)(x-13)(x+3) positive: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(-8,-3\right)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(13,\infty\right)\">\r<BR>\n" );
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document.write( "So combine them with a union symbol to get the final answer: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(-8,-3\right)\cup\left(13,\infty\right)\">\r<BR>\n" );
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document.write( "Here's a graph to visually confirm this\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-10%2C+18%2C+-1200%2C+1000%2C+%28x%2B8%29%28x-13%29%28x%2B3%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+18%2C+-1200%2C+1000%2C+%28x%2B8%29%28x-13%29%28x%2B3%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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