document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1012085>Question 1012085</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have to factor the polynomial completely (a) over the real numbers, and (b) over the complex numbers.<BR>\n" );
document.write( "X to the third power + 4x to the second power + 5x\r<BR>\n" );
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document.write( "I started with x(x squared +4x+5) i know that x=0 is a real root. But there are no real factors of 5 that add up to 4? So what do i do? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #627937 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</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=627937\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2B+4x+%5E2%2B+5x ALIGN=MIDDLE  ALT=\"x%5E3%2B+4x+%5E2%2B+5x\"   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=x%28x%5E2%2B+4x+%2B+5%29 ALIGN=MIDDLE  ALT=\"x%28x%5E2%2B+4x+%2B+5%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=x%28x%5E2%2B+4x+%2B+5%29 ALIGN=MIDDLE  ALT=\"x%28x%5E2%2B+4x+%2B+5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >......use quadratic formula to find the roots of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B+4x+%2B+5 ALIGN=MIDDLE  ALT=\"x%5E2%2B+4x+%2B+5\"   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=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%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=x+=+%28-4+%2B-+sqrt%28+4%5E2-4%2A1%2A5+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-4+%2B-+sqrt%28+4%5E2-4%2A1%2A5+%29%29%2F%282%2A1%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=x+=+%28-4+%2B-+sqrt%28+16-20+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-4+%2B-+sqrt%28+16-20+%29%29%2F2+\"   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=x+=+%28-4+%2B-+sqrt%28+-4+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-4+%2B-+sqrt%28+-4+%29%29%2F2+\"   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=x+=+%28-4+%2B-+2i%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-4+%2B-+2i%29%2F2+\"   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=x+=+%28-cross%284%292+%2B-+cross%282%29i%29%2Fcross%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-cross%284%292+%2B-+cross%282%29i%29%2Fcross%282%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=x+=+%282+%2B-i%29+ ALIGN=MIDDLE  ALT=\"x+=+%282+%2B-i%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "roots: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%282+%2Bi%29+ ALIGN=MIDDLE  ALT=\"x+=+%282+%2Bi%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%282+-i%29+ ALIGN=MIDDLE  ALT=\"x+=+%282+-i%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "use their product rule and you have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B+%282+%2Bi%29%29 ALIGN=MIDDLE  ALT=\"%28x%2B+%282+%2Bi%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B%282+-i%29%29+ ALIGN=MIDDLE  ALT=\"%28x%2B%282+-i%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, to continue with factoring, we have\r<BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x%2B+%282+%2Bi%29%29%28x%2B%282+-i%29%29 ALIGN=MIDDLE  ALT=\"x%28x%2B+%282+%2Bi%29%29%28x%2B%282+-i%29%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=x%28x%2B+2+%2Bi%29%28x%2B2+-i%29 ALIGN=MIDDLE  ALT=\"x%28x%2B+2+%2Bi%29%28x%2B2+-i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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