document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1169630>Question 1169630</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the maximum number of real zeros for the equation f(x)=x^3+7x^2+8x-16<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #794408 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=794408\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E3%2B7x%5E2%2B8x-16 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E3%2B7x%5E2%2B8x-16\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........factor completely, write <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%5E2 ALIGN=MIDDLE  ALT=\"7x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > as<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-x%5E2%2B8x%5E2+ ALIGN=MIDDLE  ALT=\"+-x%5E2%2B8x%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x ALIGN=MIDDLE  ALT=\"8x\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8x%2B16x ALIGN=MIDDLE  ALT=\"-8x%2B16x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E3-x%5E2%2B8x%5E2-8x%2B16x-16 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E3-x%5E2%2B8x%5E2-8x%2B16x-16\"   DISABLED_style= \"max-width:90%; height:auto;\" >...group\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x%5E3-x%5E2%29%2B%288x%5E2-8x%29%2B%2816x-16%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%5E3-x%5E2%29%2B%288x%5E2-8x%29%2B%2816x-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...factor out common\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E2%28x-1%29%2B8x%28x-1%29%2B16%28x-1%29 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E2%28x-1%29%2B8x%28x-1%29%2B16%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x+-+1%29+%28x%5E2+%2B+8+x+%2B+16%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x+-+1%29+%28x%5E2+%2B+8+x+%2B+16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x+-+1%29+%28x%5E2+%2B+8+x+%2B+4%5E2%29+ ALIGN=MIDDLE  ALT=\"f%28x%29=%28x+-+1%29+%28x%5E2+%2B+8+x+%2B+4%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >........use square of sum rule\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29=%28x+-+1%29+%28x+%2B+4%29%5E2 ALIGN=MIDDLE  ALT=\"+f%28x%29=%28x+-+1%29+%28x+%2B+4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "real zeros are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+1%29+%28x+%2B+4%29%5E2=0 ALIGN=MIDDLE  ALT=\"%28x+-+1%29+%28x+%2B+4%29%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+1%29=0 ALIGN=MIDDLE  ALT=\"%28x+-+1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=1%29 ALIGN=MIDDLE  ALT=\"highlight%28x=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+4%29%5E2=0 ALIGN=MIDDLE  ALT=\"%28x+%2B+4%29%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=-4%29 ALIGN=MIDDLE  ALT=\"highlight%28x=-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> double root\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E3%2B7x%5E2%2B8x-16%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E3%2B7x%5E2%2B8x-16%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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