document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1148192>Question 1148192</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two polynomials P and D are given. Use either synthetic or long division to divide <BR>\n" );
document.write( "P(x)  by  D(x),<BR>\n" );
document.write( " and express P in the form <BR>\n" );
document.write( "P(x) = D(x) · Q(x) + R(x)\r<BR>\n" );
document.write( "\n" );
document.write( "P(x) = 64x^5 − 16x^4 + 4x^2 − 4,    D(x) = 4x^2 − 4x + 1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #769551 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=769551\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Synthetic division can only be used to divide a polynomial by a linear binomial; you need to use long division.<br><BR>\n" );
document.write( "Do you not know how to do polynomial long division?  Here is an example.<br><PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
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document.write( "                                 2x  +  3\r\n" );
document.write( "                -------------------------\r\n" );
document.write( "  3x^2 - 2x + 5 )  6x^3 + 5x^2 +  6x + 20\r\n" );
document.write( "                   6x^3 - 4x^2 + 10x\r\n" );
document.write( "                   ----------------------\r\n" );
document.write( "                          9x^2 -  4x + 20\r\n" );
document.write( "                          9x^2 -  6x + 15\r\n" );
document.write( "                          ---------------\r\n" );
document.write( "                                  2x +  5</PRE><BR>\n" );
document.write( "6x^3+5x^2+6x+20, divided by 3x^2-2x+5, is 2x+3 with remainder 2x+5.  Or, in the form required in your problem,<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E3%2B5x%5E2%2B6x%2B20+=+%283x%5E2-2x%2B5%29%282x%2B3%29+%2B+%282x%2B5%29 ALIGN=MIDDLE  ALT=\"6x%5E3%2B5x%5E2%2B6x%2B20+=+%283x%5E2-2x%2B5%29%282x%2B3%29+%2B+%282x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );