document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=177074>Question 177074</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When x^3+cx+d is divided by x+1, the remainder is 3, and when it is divided by x-2, the remainder is -3. Determine the values of c and d. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #132135 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=132135\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You need to use polynomial long division to divide <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+%2B+cx+%2B+d ALIGN=MIDDLE  ALT=\"x%5E3+%2B+cx+%2B+d\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+1 ALIGN=MIDDLE  ALT=\"x+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Remember to include the missing <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;\" > term, so your dividend becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+%2B+0x%5E2+%2B+cx+%2B+d ALIGN=MIDDLE  ALT=\"x%5E3+%2B+0x%5E2+%2B+cx+%2B+d\"   DISABLED_style= \"max-width:90%; height:auto;\" >.   Rendering polynomial long division on this site is very difficult, so I'm just going to hope you know how to do that.  You will find that the remainder is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+-+%28c+%2B+1%29 ALIGN=MIDDLE  ALT=\"d+-+%28c+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which you are told is equal to 3.\r<BR>\n" );
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document.write( "Do the polynomial long division again, this time using <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+2 ALIGN=MIDDLE  ALT=\"x+-+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > as a divisor and you will discover that the remainder is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+%2B+2%28c+%2B+4%29 ALIGN=MIDDLE  ALT=\"d+%2B+2%28c+%2B+4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which you are told is equal to -3.\r<BR>\n" );
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document.write( "Now you have two 2-variable linear equations:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+-+c+-+1+=+3 ALIGN=MIDDLE  ALT=\"d+-+c+-+1+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+-+c+=+4 ALIGN=MIDDLE  ALT=\"d+-+c+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+%2B+2c+%2B+8+=+-3 ALIGN=MIDDLE  ALT=\"d+%2B+2c+%2B+8+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+%2B+2c+=+-11 ALIGN=MIDDLE  ALT=\"d+%2B+2c+=+-11\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solve this system for c and d to get your answer. </SPAN>\n" );
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