document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=124827>Question 124827</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you solve for m^3+3m^2-7m-21 divided by m^2-7? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #91519 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=91519\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What you need to do is polynomial long division.  The process is difficult to render on this system, so follow along carefully.\r<BR>\n" );
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document.write( "The first thing that you have to recognize is that there is no <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m ALIGN=MIDDLE  ALT=\"m\"   DISABLED_style= \"max-width:90%; height:auto;\" > term in your divisor.  So you have to re-write the divisor to be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5E2%2B0m-7 ALIGN=MIDDLE  ALT=\"m%5E2%2B0m-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Divide the lead term of the divisor into the lead term of the dividend.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5E2 ALIGN=MIDDLE  ALT=\"m%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > goes into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5E3 ALIGN=MIDDLE  ALT=\"m%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m ALIGN=MIDDLE  ALT=\"m\"   DISABLED_style= \"max-width:90%; height:auto;\" > times.  Write down <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m ALIGN=MIDDLE  ALT=\"m\"   DISABLED_style= \"max-width:90%; height:auto;\" > as the first term of your quotient.\r<BR>\n" );
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document.write( "Multiply the first term of your quotient, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m ALIGN=MIDDLE  ALT=\"m\"   DISABLED_style= \"max-width:90%; height:auto;\" > by each term of the divisior and put your results under the dividend, lining up like terms.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m ALIGN=MIDDLE  ALT=\"m\"   DISABLED_style= \"max-width:90%; height:auto;\" > times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7 ALIGN=MIDDLE  ALT=\"-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7m ALIGN=MIDDLE  ALT=\"-7m\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m ALIGN=MIDDLE  ALT=\"m\"   DISABLED_style= \"max-width:90%; height:auto;\" > times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0m ALIGN=MIDDLE  ALT=\"0m\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0m%5E2 ALIGN=MIDDLE  ALT=\"0m%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and finally <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m ALIGN=MIDDLE  ALT=\"m\"   DISABLED_style= \"max-width:90%; height:auto;\" > times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5E2 ALIGN=MIDDLE  ALT=\"m%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5E3 ALIGN=MIDDLE  ALT=\"m%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  This is your first partial product.\r<BR>\n" );
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document.write( "Subtract the first partial product from the dividend, just like when you are doing regular long division, except subtract the two polynomials term-by-term.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7m-%28-7m%29=0m ALIGN=MIDDLE  ALT=\"-7m-%28-7m%29=0m\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3m%5E2-0m%5E2=3m%5E2 ALIGN=MIDDLE  ALT=\"3m%5E2-0m%5E2=3m%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5E3-m%5E3=0 ALIGN=MIDDLE  ALT=\"m%5E3-m%5E3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "That leaves you with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3m%5E2%2B0m-21 ALIGN=MIDDLE  ALT=\"3m%5E2%2B0m-21\"   DISABLED_style= \"max-width:90%; height:auto;\" > as a partial dividend.  Divide the lead term of your divisor into the lead term of this partial dividend.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5E2 ALIGN=MIDDLE  ALT=\"m%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > goes into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3m%5E2 ALIGN=MIDDLE  ALT=\"3m%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > times.  Put a plus <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2B3 ALIGN=MIDDLE  ALT=\"%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > in your quotient.\r<BR>\n" );
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document.write( "Now multiply this <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > times the divisor, term by term.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A%28-7%29=-21 ALIGN=MIDDLE  ALT=\"3%2A%28-7%29=-21\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A0m=0m ALIGN=MIDDLE  ALT=\"3%2A0m=0m\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Am%5E2=3m%5E2 ALIGN=MIDDLE  ALT=\"3%2Am%5E2=3m%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Put this entire expression beneath your partial dividend, lining up like terms.\r<BR>\n" );
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document.write( "Now subtract.  If you have done everything correctly, you should have a result of 0.  That means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5E2-7 ALIGN=MIDDLE  ALT=\"m%5E2-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > divides, specifically <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%2B3 ALIGN=MIDDLE  ALT=\"m%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > times, into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5E3%2B3m%5E2-7m-21 ALIGN=MIDDLE  ALT=\"m%5E3%2B3m%5E2-7m-21\"   DISABLED_style= \"max-width:90%; height:auto;\" >, with no remainder.\r<BR>\n" );
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document.write( "Now we can say that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28m%2B3%29%28m%5E2-7%29=m%5E3%2B3m%5E2-7m-21 ALIGN=MIDDLE  ALT=\"%28m%2B3%29%28m%5E2-7%29=m%5E3%2B3m%5E2-7m-21\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Multiply it out to check the answer.  </SPAN>\n" );
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