document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=550005>Question 550005</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use synthetic division to determine which pair of integers provide both a lower and an upper bound for the zeros of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28X%29=2X%5E4-X%5E3-23X%5E2%2B46X-24 ALIGN=MIDDLE  ALT=\"f%28X%29=2X%5E4-X%5E3-23X%5E2%2B46X-24\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #358287 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=358287\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(X)=2X^4-X^3-23X^2+46X-24 <BR>\n" );
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document.write( "The coefficients add up to zero, so x = 1 is a root:<BR>\n" );
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document.write( "Use synthetic division to help find the 2 remaining roots:<BR>\n" );
document.write( "1)...2....-1....-23.....46.....-24<BR>\n" );
document.write( "......2.....1.....-22....24....|..0<BR>\n" );
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document.write( "Quotient: 2x^3+x^2-22x+24<BR>\n" );
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document.write( "I graphed the cubic and found a zero at x = 3/2<BR>\n" );
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document.write( "(3/2))....2....1....-22....24<BR>\n" );
document.write( "...........2....4.....-16...|0<BR>\n" );
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document.write( "Quotient: 2x^2+4x-16<BR>\n" );
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document.write( "Factor:<BR>\n" );
document.write( "= 2(x^2+2x-8)<BR>\n" );
document.write( "= 2(x+4)(x-2)<BR>\n" );
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document.write( "The roots are 1, 3/2 , 2 , -4<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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