document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=825059>Question 825059</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let P(x)= 2x^3-5x^2-4x+3\r<BR>\n" );
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document.write( "Find the complete factorization of P.\r<BR>\n" );
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document.write( "I think this needs to be a Polynomial but I'm not sure where to begin.  I understand how to do everything else with the equation.  This one kind of screws me up.  Please help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #496985 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=496985\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We are looking for factors which are the 0's of 2x^3-5x^2-4x+3<BR>\n" );
document.write( "I start by looking for rational roots and of course, 1 or -1 is worth checking first<BR>\n" );
document.write( "if x = 1, we get 2 -5 -4 +3 = -4 so 1 is not a 0<BR>\n" );
document.write( "if x = -1, we get -2 -5 +4 +3 = 0 so -1 is a 0 and x+1 is a factor.  Now use synthetic division<BR>\n" );
document.write( "-1 | 2  -5  -4  3  |<BR>\n" );
document.write( "   |    -2   7 -3  |            |<BR>\n" );
document.write( "   | 2  -7   3  0  |<BR>\n" );
document.write( "This leaves us with the smaller polynomial 2x^2 -7x +3 and we can factor this smaller polynomial into (2x-1) * (x-3),  therefore the complete factorization of<BR>\n" );
document.write( "2x^3-5x^2-4x+3 is (x+1)*(2x-1)*(x-3)<BR>\n" );
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