document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=31461>Question 31461</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I solve the equation:  2u^4-5u^3-12u^2+2u-8 divided by u-4 ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #18156 by </B><A HREF=/tutors/aboutme.mpl?userid=Cintchr><B>Cintchr(481)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Cintchr><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=18156\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%282u%5E4-5u%5E3-12u%5E2%2B2u-8%29%2F%28u-4%29+ ALIGN=MIDDLE  ALT=\"+%282u%5E4-5u%5E3-12u%5E2%2B2u-8%29%2F%28u-4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "When dividing by a binomial you MUST make sure that the numerator is in decending order, and that there are no missing exponential values.<BR>\n" );
document.write( "This numerator meets that criteria.<BR>\n" );
document.write( "Now ... I have not found a way to show the long division in the rendering page so this may seem really long, but bear with me and we will take it all step by step.<BR>\n" );
document.write( "FIRST: look at the denominator.  you are going to divide by u first.  Ask yourself: what number times u equals 2u^4?  The answer: 2u^3<BR>\n" );
document.write( "NEXT: multiply that value times the denominator<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%282u%5E3%29+%28u-4%29+=+2u%5E4-8u%5E3+ ALIGN=MIDDLE  ALT=\"+highlight%282u%5E3%29+%28u-4%29+=+2u%5E4-8u%5E3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract this value from the numerator ...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%282u%5E4-5u%5E3-12u%5E2%2B2u-8%29+-+%282u%5E4-8u%5E3%29+ ALIGN=MIDDLE  ALT=\"+%282u%5E4-5u%5E3-12u%5E2%2B2u-8%29+-+%282u%5E4-8u%5E3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > dont forget to distribute the negative<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2u%5E4-5u%5E3-12u%5E2%2B2u-8-2u%5E4%2B8u%5E3+ ALIGN=MIDDLE  ALT=\"+2u%5E4-5u%5E3-12u%5E2%2B2u-8-2u%5E4%2B8u%5E3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "When you combine like terms ...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3u%5E3-12u%5E2%2B2u-8+ ALIGN=MIDDLE  ALT=\"+3u%5E3-12u%5E2%2B2u-8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "notice that the first term cancels.  We did this on purpose.<BR>\n" );
document.write( "continue on as we did in the the first step, this time asking: what number times u equals 3u^3?  The answer: 3u^2<BR>\n" );
document.write( "Multiply that value by the denominator.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%283u%5E2%29+%28u-4%29+=+3u%5E3-12u%5E2+ ALIGN=MIDDLE  ALT=\"+highlight%283u%5E2%29+%28u-4%29+=+3u%5E3-12u%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > subtract this answer once again.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3u%5E3-12u%5E2%2B2u-8+-+%283u%5E3-12u%5E2%29+ ALIGN=MIDDLE  ALT=\"+3u%5E3-12u%5E2%2B2u-8+-+%283u%5E3-12u%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > watch the negatives<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3u%5E3-12u%5E2%2B2u-8-3u%5E3%2B12u%5E2+ ALIGN=MIDDLE  ALT=\"+3u%5E3-12u%5E2%2B2u-8-3u%5E3%2B12u%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > combine like terms.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-12u%5E2%2B2u-8%2B12u%5E2+ ALIGN=MIDDLE  ALT=\"+-12u%5E2%2B2u-8%2B12u%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > notice that TWO terms will cancel in this step<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2u-8+ ALIGN=MIDDLE  ALT=\"+2u-8+\"   DISABLED_style= \"max-width:90%; height:auto;\" > back to step one:<BR>\n" );
document.write( "What number times u equals 2u?  The answer is 2.<BR>\n" );
document.write( "Multiply it by the denominator.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%282%29%28u-4%29+=+2u-8+ ALIGN=MIDDLE  ALT=\"+highlight%282%29%28u-4%29+=+2u-8+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Subtract this value from what remains.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2u-8+-+%282u-8%29+ ALIGN=MIDDLE  ALT=\"+2u-8+-+%282u-8%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > watch the negatives ....<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2u+-8+-+2u+%2B+8+ ALIGN=MIDDLE  ALT=\"+2u+-8+-+2u+%2B+8+\"   DISABLED_style= \"max-width:90%; height:auto;\" > EVERYTHING cancels.<BR>\n" );
document.write( "This means there is NO remainder.<BR>\n" );
document.write( "Lets look at the numbers we came up with in each \"First step\" (the highlighted numbers)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2u%5E3+ ALIGN=MIDDLE  ALT=\"+2u%5E3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3u%5E2+ ALIGN=MIDDLE  ALT=\"+3u%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2+ ALIGN=MIDDLE  ALT=\"+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Add these numbers together<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2u%5E3+%2B+3u%5E2+%2B+2+ ALIGN=MIDDLE  ALT=\"+2u%5E3+%2B+3u%5E2+%2B+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > this is your answer\r<BR>\n" );
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