document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209688>Question 1209688</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The polynomial\r<BR>\n" );
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document.write( "f(x) = x^3 + 10x^2 + 21x + 10 + 4x^3 - 17x^2 + 8x - 66\r<BR>\n" );
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document.write( "has one integer root.  What is it? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849823 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52866)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849823\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "I made a plot, using the plotting tool DESMOS at www.desmos.com/calculator,<BR>\n" );
document.write( "which is free of charge online plotting tool for common use.\r<BR>\n" );
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document.write( "See the plot under this link\r<BR>\n" );
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document.write( "https://www.desmos.com/calculator/07tfoacyi9\r<BR>\n" );
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document.write( "The plot shows absence of integer roots.\r<BR>\n" );
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document.write( "<H3>The CONCLUSION and the DIAGNOSIS</H3>This post is not a Math problem, but a FATAL GIBBERISH, instead.\r<BR>\n" );
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document.write( "/\/\/\/\/\/\/\/\/\/\ &nbsp;&nbsp;Second attempt &nbsp;&nbsp;/\/\/\/\/\/\/\/\/\/\\r<BR>\n" );
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document.write( "The polynomial\r<BR>\n" );
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document.write( "f(x) = x^3 + 10x^2 + 21x + 10 + 4x^3 - 17x^2 + 8x - 66\r<BR>\n" );
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document.write( "has one integer root.  What is it?<BR>\n" );
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document.write( "1. Combine like terms:\r\n" );
document.write( "   f(x) = (x^3 + 4x^3) + (10x^2 - 17x^2) + (21x + 8x) + (10 - 66)\r\n" );
document.write( "   f(x) = 5x^3 - 7x^2 + 29x - 56\r\n" );
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document.write( "2. Rational Root Theorem: This theorem states that any rational root of the polynomial must be of the form p/q, \r\n" );
document.write( "   where p is a factor of the constant term (-56) and q is a factor of the leading coefficient (5).\r\n" );
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document.write( "   Possible values for p: ±1, ±2, ±4, ±7, ±8, ±14, ±28, ±56\r\n" );
document.write( "   Possible values for q: ±1, ±5\r\n" );
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document.write( "   Possible rational roots: ±1, ±2, ±4, ±7, ±8, ±14, ±28, ±56, ±1/5, ±2/5, ±4/5, ±7/5, ±8/5, ±14/5, ±28/5, ±56/5\r\n" );
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document.write( "   Possible integer roots: ±1, ±2, ±4, ±7, ±8, ±14, ±28, ±56.\r\n" );
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document.write( "3. I checked all these possible integer roots using my MS Excel.\r\n" );
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document.write( "   NO ONE of this values is a root of the polynomial 5x^3 - 7x^2 + 29x - 56.\r\n" );
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document.write( "<H3>It means that your problem is a FAKE: it DECEIVES a reader.</H3>\r<BR>\n" );
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document.write( "<U>ANSWER</U>.  &nbsp;&nbsp;This problem is a &nbsp;FAKE : &nbsp;&nbsp;it deceives a reader and presents a &nbsp;FALSE &nbsp;situation as if it is true.\r<BR>\n" );
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document.write( "         The given polynomial &nbsp;HAS &nbsp;NO &nbsp;integer roots.  &nbsp;&nbsp;No one integer number is a root of this polynomial.\r<BR>\n" );
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document.write( "<H3>The answer in the post by @CPhill is INCORRECT (= WRONG).</H3>\r<BR>\n" );
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