document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=442319>Question 442319</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how is dividing a polynomial by a binomial similar to or different from the long division you learn in elementary school? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #305056 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><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=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=305056\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's start off basic. Let's say you are dividing 4 into 43.\r<BR>\n" );
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document.write( "then 4 | 43     How many times does 4 go into 4?  1. So take 4*1 and subtract it from your first spot. Giving you:  How many times does 4 | 3?  0. So we multiply 4 by 0 and add the 3. Since we'd keep repeating the process we'd say the answer is 10, with a remainder of 3. This 3 can also be written as  3/4, the remainder over the divisor.\r<BR>\n" );
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document.write( "Let's apply this to polynomial division.\r<BR>\n" );
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document.write( "Divide  x+1 into 2x^2+4x-3.\r<BR>\n" );
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document.write( "How many times does x go into 2x^2?  <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.\r<BR>\n" );
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document.write( "so 2x(x+1) = 2x^2 +2x and so we subtract that from our original.\r<BR>\n" );
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document.write( "So we are left with 2x -3.  We play the same game. How many times does x go into 2x?  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > times. \r<BR>\n" );
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document.write( "So we take 2(x+1)  = 2x+2 and we subtract that from our last total.  so [2x-3] - [2x+2] = -5.\r<BR>\n" );
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document.write( "We are left with a remainder of -5, but just like we did in our \"numerical\" example, we can write the remainder as a fraction. In this case, -5/x+1.\r<BR>\n" );
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document.write( "So our complete answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+%2B2+-+%285%2F%28x%2B1%29%29 ALIGN=MIDDLE  ALT=\"2x+%2B2+-+%285%2F%28x%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for this made up problem. It's the same process, just they're xs. </SPAN>\n" );
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