document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1163109>Question 1163109</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I don't know how to answer this because as far as I know this is not factorable, but the question seems to say that it is.\r<BR>\n" );
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document.write( "David’s homework was to factor the polynomial completely (a) over the real numbers, (b) over the complex numbers.\r<BR>\n" );
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document.write( "x^3+4x^2+5x\r<BR>\n" );
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document.write( "He started x(x^2+4x+5) He knows that x=0 is a real root.<BR>\n" );
document.write( "But there are no real factors of 5 that add up to 4???? So what does he do? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #787088 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=787088\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "At the point where you have<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2B4x%5E2%2B45+=+x%28x%5E2%2B4x%2B5%29 ALIGN=MIDDLE  ALT=\"x%5E3%2B4x%5E2%2B45+=+x%28x%5E2%2B4x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "you are finished with part (a); the remaining quadratic factor does not factor over the real numbers.<br><BR>\n" );
document.write( "However, every quadratic expression factors over the complex numbers; so you can do part (b).  Solve the equation<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B4x%2B5+=+0 ALIGN=MIDDLE  ALT=\"x%5E2%2B4x%2B5+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "using the quadratic formula.  That gives you the roots of the quadratic equation; therefore it shows you how to factor the quadratic over the complex numbers.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-4+%2B+sqrt%2816-20%29%29%2F2+=+-2%2Bi ALIGN=MIDDLE  ALT=\"x+=+%28-4+%2B+sqrt%2816-20%29%29%2F2+=+-2%2Bi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "and<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-4+-+sqrt%2816-20%29%29%2F2+=+-2-i ALIGN=MIDDLE  ALT=\"x+=+%28-4+-+sqrt%2816-20%29%29%2F2+=+-2-i\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B4x%2B5+=+%28x-%28-2%2Bi%29%29%28x-%28-2-i%29%29 ALIGN=MIDDLE  ALT=\"x%5E2%2B4x%2B5+=+%28x-%28-2%2Bi%29%29%28x-%28-2-i%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "And so, finally,<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2B4x%5E2%2B5x+=+%28x%29%28x-%28-2%2Bi%29%29%28x-%28-2-i%29%29 ALIGN=MIDDLE  ALT=\"x%5E3%2B4x%5E2%2B5x+=+%28x%29%28x-%28-2%2Bi%29%29%28x-%28-2-i%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
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