document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=24417>Question 24417</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please show me step by step how to divide:\r<BR>\n" );
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document.write( "(x^3 + 5x^2 - 10) by (x + 3)\r<BR>\n" );
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document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #12999 by </B><A HREF=/tutors/aboutme.mpl?userid=kev82><B>kev82(151)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=kev82><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=12999\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi,\r<BR>\n" );
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document.write( "When I first learnt to do this, I found it really hard. But if you keep practicing it will become second nature, trust me.\r<BR>\n" );
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document.write( "Before I go through your problem let me point you to <a  rel=nofollow HREF=\"http://www.purplemath.com/modules/polydiv2.htm\">this really good explanation</a>. If you can follow that and do the practice ones on there, then you should find this easy.\r<BR>\n" );
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document.write( "I would like to draw the division out as I do it, but it would take me hours to type it in here, so we'll see how you get on. If you still can't do it email me and I'll write it down on paper and scan it in for you.\r<BR>\n" );
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document.write( "How many times does <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3 ALIGN=MIDDLE  ALT=\"x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > go into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3 ALIGN=MIDDLE  ALT=\"x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >? The answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29x%5E2=x%5E3%2B3x%5E2 ALIGN=MIDDLE  ALT=\"%28x%2B3%29x%5E2=x%5E3%2B3x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So we know the answer has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > in it, and we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+%2B+5x%5E2+-+10+-+%28x%5E3%2B3x%5E2%29+=+2x%5E2+-10 ALIGN=MIDDLE  ALT=\"x%5E3+%2B+5x%5E2+-+10+-+%28x%5E3%2B3x%5E2%29+=+2x%5E2+-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > left.\r<BR>\n" );
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document.write( "So we now need to work out <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-10 ALIGN=MIDDLE  ALT=\"2x%5E2-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > divided by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3 ALIGN=MIDDLE  ALT=\"x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Asking the same question as before we can see that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3 ALIGN=MIDDLE  ALT=\"x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > goes into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2 ALIGN=MIDDLE  ALT=\"2x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x ALIGN=MIDDLE  ALT=\"2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > times. The remainder is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-10+-+2x%28x%2B3%29=-6x-10 ALIGN=MIDDLE  ALT=\"2x%5E2-10+-+2x%28x%2B3%29=-6x-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So we know that the final answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > plus <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x ALIGN=MIDDLE  ALT=\"2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > plus <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6x-10 ALIGN=MIDDLE  ALT=\"-6x-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > divided by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3 ALIGN=MIDDLE  ALT=\"x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Repeating the same process <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3 ALIGN=MIDDLE  ALT=\"x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > goes into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6x-10 ALIGN=MIDDLE  ALT=\"-6x-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6 ALIGN=MIDDLE  ALT=\"-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > times, with remainder <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6x-10+-+-6%28x%2B3%29=8 ALIGN=MIDDLE  ALT=\"-6x-10+-+-6%28x%2B3%29=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >. At this point we stop because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3 ALIGN=MIDDLE  ALT=\"x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > doesn't go into 8. So the final answer is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x-6%2B8%2F%28x%2B3%29 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x-6%2B8%2F%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The last term is the remainder, because there isn't anything else we can do with it. Don't forget to check your answer is right by multiplying that by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3 ALIGN=MIDDLE  ALT=\"x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and checking you get the original expression.\r<BR>\n" );
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document.write( "Hope that helps, and if you need me to send you the working written down, then please email back.\r<BR>\n" );
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document.write( "Kev </SPAN>\n" );
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