document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=469092>Question 469092</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the rational zero theorem to find all rational roots of the given equation.\r<BR>\n" );
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document.write( "3x^-x^-3x+1=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #322075 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=322075\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use the rational zero theorem to find all rational roots of the given equation. <BR>\n" );
document.write( "3x^-x^-3x+1=0<BR>\n" );
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document.write( "p(x)=3x^3-x^2-3x+1=0<BR>\n" );
document.write( "factors of p=1:...±1<BR>\n" );
document.write( "factors of q=3:....±1, ±3<BR>\n" );
document.write( "possible rational roots: ±1, ±1/3<BR>\n" );
document.write( "Using synthetic division to find roots<BR>\n" );
document.write( "0) ..... 3....-1....-3....1<BR>\n" );
document.write( "1) ..... 3......2....-1....0 (root=1)<BR>\n" );
document.write( "p(x)=(x-1)(3x^2+2x-1)<BR>\n" );
document.write( "p(x)=(x-1)(3x-1)(x+1)<BR>\n" );
document.write( "roots: -1, 1/3, 1 </SPAN>\n" );
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