document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=78550>Question 78550</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I keep trying on this problem and I'm running out of time and sanity.  Please for the love of God, help me.  x5+24>3x3+8x2.  I can't even figure out how to write it on the computer. That should be x to the power of 5, plus 24 > 3x to the power of 3 plus 8x squared.  I understand that you need to bring everything over to equal 0.  I have found one factor of it too, (x-2) but can't completely solve.  Thanks so much!    </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #56329 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=56329\">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%5E5%2B24%3E3x%5E3%2B8x%5E2 ALIGN=MIDDLE  ALT=\"x%5E5%2B24%3E3x%5E3%2B8x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E5-3x%5E3-8x%5E2%2B24%3E0 ALIGN=MIDDLE  ALT=\"x%5E5-3x%5E3-8x%5E2%2B24%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Get all terms to one side<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%28x%5E2-3%29-8%28x%5E2-3%29%3E0 ALIGN=MIDDLE  ALT=\"x%5E3%28x%5E2-3%29-8%28x%5E2-3%29%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E3-8%29%28x%5E2-3%29%3E0 ALIGN=MIDDLE  ALT=\"%28x%5E3-8%29%28x%5E2-3%29%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E3-8%29%28x%5E2-3%29=0 ALIGN=MIDDLE  ALT=\"%28x%5E3-8%29%28x%5E2-3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now make an equation\r<BR>\n" );
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document.write( "Set each factor equal to zero<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3-8=0 ALIGN=MIDDLE  ALT=\"x%5E3-8=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-2%29%28x%5E2%2B2x%2B4%29=0 ALIGN=MIDDLE  ALT=\"%28x-2%29%28x%5E2%2B2x%2B4%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > use the difference of cubes<BR>\n" );
document.write( "Set x-2 equal to zero<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2=0 ALIGN=MIDDLE  ALT=\"x-2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Set <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x%2B4 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > equal to zero<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x%2B4=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x%2B4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This cannot be factored further\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now set <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-3 ALIGN=MIDDLE  ALT=\"x%5E2-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > equal to zero\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-3=0 ALIGN=MIDDLE  ALT=\"x%5E2-3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=3 ALIGN=MIDDLE  ALT=\"x%5E2=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0%2B-sqrt%283%29 ALIGN=MIDDLE  ALT=\"x=0%2B-sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%283%29 ALIGN=MIDDLE  ALT=\"x=sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-sqrt%283%29 ALIGN=MIDDLE  ALT=\"x=-sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "These are the points where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E5-3x%5E3-8x%5E2%2B24 ALIGN=MIDDLE  ALT=\"x%5E5-3x%5E3-8x%5E2%2B24\"   DISABLED_style= \"max-width:90%; height:auto;\" > goes through the x-axis. These are the turning points from positive to negative or vice versa. In other words, at these points the graph will change from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29%3E0 ALIGN=MIDDLE  ALT=\"f%28x%29%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29%3C0 ALIGN=MIDDLE  ALT=\"f%28x%29%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or vice versa. So lets graph the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E5-3x%5E3-8x%5E2%2B24 ALIGN=MIDDLE  ALT=\"y=x%5E5-3x%5E3-8x%5E2%2B24\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2Cx%5E5-3x%5E3-8x%5E2%2B24%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2Cx%5E5-3x%5E3-8x%5E2%2B24%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "From the graph we can see that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29%3E0 ALIGN=MIDDLE  ALT=\"f%28x%29%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the interval\r<BR>\n" );
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document.write( "[<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%283%29 ALIGN=MIDDLE  ALT=\"-sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29 ALIGN=MIDDLE  ALT=\"sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >] U [2,<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \infty\">)\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );