document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=86378>Question 86378</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with this:  find the polynomial written as a product of linear factors:  f(x)=2x^3+5x^2-11x+4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #62494 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=62494\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> find the polynomial written as a product of linear factors:  f(x)=2x^3+5x^2-11x+4<BR>\n" );
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document.write( "Because the coefficients add up to zero, x=1 is a root; so (x-1) is a factor.<BR>\n" );
document.write( "Using synthetic division you get:<BR>\n" );
document.write( "1)2....5....-11....4<BR>\n" );
document.write( "....2....7.....-4..|..0\r<BR>\n" );
document.write( "\n" );
document.write( "=========<BR>\n" );
document.write( "Remainder = 0<BR>\n" );
document.write( "Quotient = 2x^2+7x-4<BR>\n" );
document.write( "Factor the quotient:<BR>\n" );
document.write( "2x^2-8x+x-4<BR>\n" );
document.write( "2x(x-4)+(x-4)<BR>\n" );
document.write( "(x-4)(2x+1)<BR>\n" );
document.write( "===============<BR>\n" );
document.write( "Therefore f(x) = (x-1)(x-4)(2x+1)<BR>\n" );
document.write( "==============<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );