document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=319327>Question 319327</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given that -1 is a zero of the polynomial g(x)=x^3-3x^2-3x+1, express g(x) as a product of linear factors.<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 #228634 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=228634\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "If -1 is a zero, then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ -\ (-1)\ =\ x\ +\ 1\"> must be a factor of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large g(x)\ =\ x^3\ -\ 3x^2\ -\ 3x\ +\ 1\">\r<BR>\n" );
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document.write( "Use synthetic division or polynomial long division to divide <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x^3\ -\ 3x^2\ -\ 3x\ +\ 1\"> by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ +\ 1\">.  Too difficult to render on this site, so review the process at http://www.purplemath.com/modules/synthdiv.htm or http://www.purplemath.com/modules/polydiv2.htm\r<BR>\n" );
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document.write( "The quotient comes out to be <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x^2\ -\ 4x\ +\ 1\">\r<BR>\n" );
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document.write( "Use the quadratic formula to determine the roots of the quotient polynomial are <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ 2\ \pm\ \sqrt{3}\">.  Verification is left as an exercise for the student.\r<BR>\n" );
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document.write( "Hence the remaining two factors of the original polynomial are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ -\ \left(2\ +\ \sqrt{3}\right)\">\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ -\ \left(2\ -\ \sqrt{3}\right)\">\r<BR>\n" );
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document.write( "So:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^3\ -\ 3x^2\ -\ 3x\ +\ 1\ =\ \left(x\ +\ 1\right)\left(x\ -\ 2\ -\ \sqrt{3}\right)\left(x\ -\ 2\ +\ \sqrt{3}\right)\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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