document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=21889>Question 21889</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For the polynomial function f(x) = x^4 - x^3 - 2x^2 - 4x - 24\r<BR>\n" );
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document.write( "Find all real zeroes (x-intercepts)\r<BR>\n" );
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document.write( "Divide all real zeroes out using synthetic division\r<BR>\n" );
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document.write( "solve the quadratic equation using the quadratic formula (which should give two complex zeroes)\r<BR>\n" );
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document.write( "give complete factorization of f(x)\r<BR>\n" );
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document.write( "(I know this seems long - but I am so completely lost - this one question will explain about a half 'o dozen problems I am having with my homework) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #10566 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=10566\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x) = x^4 - x^3 - 2x^2 - 4x - 24 ...TRY ,F(0),F(10,F(-1),F(2)...ETC....WE NOTE THAT F(-2) IS ZERO SO X+2  IS A FACTOR...LET US DIVIDE WITH X+2 USING HORNERS SHORT DIVISION.PLEASE COME BACK IF YOU ARE NOT CONVERSANT WITH THIS DIVISION...\r<BR>\n" );
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document.write( "-2....|1....-1....-2....-4....-24...........................................<BR>\n" );
document.write( "......|0....-2.....6....-8.....24............................................<BR>\n" );
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document.write( "......|1....-3.....4....-12.....0<BR>\n" );
document.write( "HENCE QUOTIENT IS <BR>\n" );
document.write( "X^3-3X^2+4X-12......WE FIND THAT F(3) IS ZERO...SO X-3 IS A FACTOR..AGAIN DIVIDING <BR>\n" );
document.write( "WITH X-3 WE GET\r<BR>\n" );
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document.write( "3.....|1....-3.....4....-12.....<BR>\n" );
document.write( "......|0....3......0.....12.....<BR>\n" );
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document.write( "......|1....0......4.....0<BR>\n" );
document.write( "HENCE QUOTIENT IS <BR>\n" );
document.write( "X^2+4<BR>\n" );
document.write( "=(X)^2-(2I)^2<BR>\n" );
document.write( "=(X+2I)(X-2I)<BR>\n" );
document.write( "HENCE COMPLETE FACTORISATION IS \r<BR>\n" );
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document.write( "f(x) = x^4 - x^3 - 2x^2 - 4x - 24 .=(X+2)(X-3)(X+2I)(X-2I)...THE ROOTS OR X INTERCEPTS ARE ....-2,3,2I AND -2I </SPAN>\n" );
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