document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=30941>Question 30941</A>: <I><SPAN STYLE=\"word-break: break-all;\"> List all the polynomials of degree exactly two in Z3[t]. Which of these are reducible, which are irreducible? <BR>\n" );
document.write( "Z stands for the integers </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #19946 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=19946\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> COEFFICIENTS SHALL BE,0,1,-1 ONLY...SINCE 2 IS SAME AS -1(MOD3),-2=1(MOD3) AND<BR>\n" );
document.write( "-3 OR 3=0(MOD3) <BR>\n" );
document.write( "HENCE GENERAL SECOND DEGREE POLYNOMIALIS IS <BR>\n" );
document.write( "AT^2+BT+C...PUTTING THE ABOVE VALUES WE GET THE FOLLOWING.REDUCIBILITY IS DETERMINED BY CHECKING WHETHER T=0 OR 1 OR -1 YIELDS ZERO VALUE FOT THE QUADRATIC.IF ZERO OCCURS IT IS REDUCIBLE..OTHERWISE NOT...LEGEND..R..REDCIBLE..NR..NOT REDUCIBLE..<BR>\n" );
document.write( "1.T^2-T-1..........NR<BR>\n" );
document.write( "2.T^2-T...........R...T=0 GIVES ZERO<BR>\n" );
document.write( "3.T^2-T+1....NR<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "4.T^2-1.....R AT T=1<BR>\n" );
document.write( "5.T^2....R AT T=0<BR>\n" );
document.write( "6.T^2+1...NR<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "7.T^2+T-1...NR<BR>\n" );
document.write( "8.T^2+T...R AT T=0<BR>\n" );
document.write( "9.T^2+T+1....R AT T=1...SINCE 3 IS 0(MOD3)<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "10.-T^2-T-1.....R AT T=1<BR>\n" );
document.write( "11.-T^2-T....R AT T=0<BR>\n" );
document.write( "12.-T^2-T+1...NR<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "13.-T^2-1.....NR<BR>\n" );
document.write( "14.-T^2....R AT T=0<BR>\n" );
document.write( "15.-T^2+1...R AT T=1<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "16.-T^2+T-1...R AT T=-1....SINCE -3=0(MOD3)<BR>\n" );
document.write( "17.-T^2+T...R AT T=0<BR>\n" );
document.write( "18.-T^2+T+1...NR<BR>\n" );
document.write( "--------------- </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );