document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=177840>Question 177840</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need your help factoring this problem...PLEASE!  <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 #132824 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=132824\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <FONT FACE=\"Times New Roman\" SIZE=\"+2\">\r<BR>\n" );
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document.write( "The first thing to do is to simplify this horror by letting <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t = x^2 +3x +1\">.\r<BR>\n" );
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document.write( "Now you can substitute giving you:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t^2 - 4t - 5\">\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -5 \times 1 = -5\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -5 + 1 = -4\">, this quadratic polynomial in <i>t</i> factors quite tidily:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (t - 5)(t + 1)\">\r<BR>\n" );
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document.write( "Now replace <i>t</i> with the original expression:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x^2 +3x +1 - 5)(x^2 +3x +1 + 1)\">\r<BR>\n" );
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document.write( "Collect terms:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x^2 +3x - 4)(x^2 +3x + 2)\">\r<BR>\n" );
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document.write( "Now since <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 4 \times (-1) = -4\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 4 - 1 = 3\"> the first factor factors to <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x + 4)(x - 1)\">\r<BR>\n" );
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document.write( "And since <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 2 \times 1 = 2\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 2 + 1 = 3\"> the second factor factors to <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x + 2)(x + 1)\">\r<BR>\n" );
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document.write( "Putting it all together:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x^2 + 3x + 1)^2 - 4(x^2 + 3x + 1)-5 = (x + 4)(x - 1)(x + 2)(x + 1)\">\r<BR>\n" );
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document.write( "And, as you might suspect, the graph shows four zeros that match the factors:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28%0D%0A600%2C600%2C-5%2C5%2C-5%2C5%2C%0D%0Agrid%281%29%2C%0D%0Agraph%28%0D%0A600%2C600%2C-5%2C5%2C-5%2C5%2C%0D%0Ay+=+%28x%5E2+%2B+3x+%2B+1%29%5E2+-+4%28x%5E2+%2B+3x+%2B+1%29-5%0D%0A%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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