document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=694174>Question 694174</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find all 12 solutions to x^12=1<BR>\n" );
document.write( "Already know 1 and -1 are solutions, but I'm not sure how to factor the equation. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #427775 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=427775\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hint: \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x^12=1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x^12 - 1 = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(x^4)^3 - 1^3 = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(x^4 - 1)((x^4)^2 + x^4*1 + 1^2) = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(x^4 - 1)(x^8 + x^4 + 1) = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(x^2 - 1)(x^2 + 1)(x^8 + x^4 + 1) = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(x - 1)(x + 1)(x^2 + 1)(x^8 + x^4 + 1) = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Note: \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "To solve x^8 + x^4 + 1 = 0, let z = x^4 to get z^2 + z + 1 = 0. Solve for z and use this to find solutions to x. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );