document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1039621>Question 1039621</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please factor completely and show a detailed solution. Thank you!\r<BR>\n" );
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document.write( "x^4 - 23x^2 + 49<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 #654391 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39630)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=654391\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=x%5E2 ALIGN=MIDDLE  ALT=\"p=x%5E2\"   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=p%5E2-23p%2B49 ALIGN=MIDDLE  ALT=\"p%5E2-23p%2B49\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "That method seems not useful.\r<BR>\n" );
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document.write( "Try Rational Roots Theorem and synthetic division to check roots -1, -7, 1, 7.\r<BR>\n" );
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document.write( "No remainders found (synthetic divisions done on paper).<BR>\n" );
document.write( "The polynomial does not have rational roots.  Binomial factors are not found.<BR>\n" );
document.write( "It does have four real but irrational roots.  Back to the substitution for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you can find them.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=x%5E2 ALIGN=MIDDLE  ALT=\"p=x%5E2\"   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=p%5E2-23p%2B49 ALIGN=MIDDLE  ALT=\"p%5E2-23p%2B49\"   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=p=%2823%2B-+3%2Asqrt%2837%29%29%2F2 ALIGN=MIDDLE  ALT=\"p=%2823%2B-+3%2Asqrt%2837%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Substitute back the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   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=0%2B-+sqrt%28%2823%2B-+3%2Asqrt%2837%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"x=0%2B-+sqrt%28%2823%2B-+3%2Asqrt%2837%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----which is FOUR values; the 0 included so that the rendering on the page will work.  I have not finished putting this into the final desired factored form. </SPAN>\n" );
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