document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1158341>Question 1158341</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When ax³ + bx² + cx - 4 is divided by (x+2), the remainder is double that obtained when the expression is divided by (x+1). Show that c can have any value and find b in terms of a.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #781267 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=781267\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( ", the remainder is double that obtained when the expression is divided by (x+1). Show that c can have any value and find b in terms of a.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E3+%2B+bx%5E2+%2B+cx+-+4 ALIGN=MIDDLE  ALT=\"ax%5E3+%2B+bx%5E2+%2B+cx+-+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > is divided by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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document.write( "..........(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2B%28b-+2a%29x%2B%28c-2b%2B4a%29 ALIGN=MIDDLE  ALT=\"ax%5E2%2B%28b-+2a%29x%2B%28c-2b%2B4a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >|<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E3+%2B+bx%5E2+%2B+cx+-+4 ALIGN=MIDDLE  ALT=\"ax%5E3+%2B+bx%5E2+%2B+cx+-+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "..........<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E3+%2B+2ax%5E2 ALIGN=MIDDLE  ALT=\"ax%5E3+%2B+2ax%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ............subtract<BR>\n" );
document.write( "..................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b-+2a%29x%5E2%2B+cx ALIGN=MIDDLE  ALT=\"%28b-+2a%29x%5E2%2B+cx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b-+2a%29x%5E2%2B2%28b-+2a%29x ALIGN=MIDDLE  ALT=\"%28b-+2a%29x%5E2%2B2%28b-+2a%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........subtract<BR>\n" );
document.write( "............................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28c-%282b-+4a%29%29x ALIGN=MIDDLE  ALT=\"%28c-%282b-+4a%29%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "............................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28c-2b%2B4a%29x-+4 ALIGN=MIDDLE  ALT=\"%28c-2b%2B4a%29x-+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "............................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28c-2b%2B4a%29x%2B2%28c-2b%2B4a%29 ALIGN=MIDDLE  ALT=\"%28c-2b%2B4a%29x%2B2%28c-2b%2B4a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........subtract<BR>\n" );
document.write( ".........................................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4-2%28c-2b%2B4a%29 ALIGN=MIDDLE  ALT=\"-4-2%28c-2b%2B4a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".........................................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4-2c%2B4b-8a ALIGN=MIDDLE  ALT=\"-4-2c%2B4b-8a\"   DISABLED_style= \"max-width:90%; height:auto;\" >->reminder\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E3+%2B+bx%5E2+%2B+cx+-+4 ALIGN=MIDDLE  ALT=\"ax%5E3+%2B+bx%5E2+%2B+cx+-+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > is divided by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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document.write( "..........(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2B%28b-+a%29x%2B%28c-b%2Ba%29 ALIGN=MIDDLE  ALT=\"ax%5E2%2B%28b-+a%29x%2B%28c-b%2Ba%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29 ALIGN=MIDDLE  ALT=\"%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >|<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E3+%2B+bx%5E2+%2B+cx+-+4 ALIGN=MIDDLE  ALT=\"ax%5E3+%2B+bx%5E2+%2B+cx+-+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "............<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E3+%2B+ax%5E2 ALIGN=MIDDLE  ALT=\"ax%5E3+%2B+ax%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ............subtract<BR>\n" );
document.write( "..................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b-+a%29x%5E2%2B+cx ALIGN=MIDDLE  ALT=\"%28b-+a%29x%5E2%2B+cx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b-+a%29x%5E2%2B%28b-+a%29x ALIGN=MIDDLE  ALT=\"%28b-+a%29x%5E2%2B%28b-+a%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........subtract<BR>\n" );
document.write( "............................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28c-%28b-+a%29%29x ALIGN=MIDDLE  ALT=\"%28c-%28b-+a%29%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "............................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28c-b%2Ba%29x-+4 ALIGN=MIDDLE  ALT=\"%28c-b%2Ba%29x-+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "............................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28c-b%2Ba%29x%2B%28c-b%2Ba%29 ALIGN=MIDDLE  ALT=\"%28c-b%2Ba%29x%2B%28c-b%2Ba%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........subtract<BR>\n" );
document.write( ".........................................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4-%28c-b%2Ba%29 ALIGN=MIDDLE  ALT=\"-4-%28c-b%2Ba%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".........................................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4-c%2Bb-a ALIGN=MIDDLE  ALT=\"-4-c%2Bb-a\"   DISABLED_style= \"max-width:90%; height:auto;\" >->reminder\r<BR>\n" );
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document.write( "the remainder <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4-2c%2B4b-8a ALIGN=MIDDLE  ALT=\"-4-2c%2B4b-8a\"   DISABLED_style= \"max-width:90%; height:auto;\" > is double more than remainder <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4-c%2Bb-a ALIGN=MIDDLE  ALT=\"-4-c%2Bb-a\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4-2c%2B4b-8a=2%28-4-c%2Bb-a%29 ALIGN=MIDDLE  ALT=\"-4-2c%2B4b-8a=2%28-4-c%2Bb-a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4-2c%2B4b-8a=-8-2c%2B2b-2a ALIGN=MIDDLE  ALT=\"-4-2c%2B4b-8a=-8-2c%2B2b-2a\"   DISABLED_style= \"max-width:90%; height:auto;\" >........simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4-cross%282c%29%2B4b-8a=-8-cross%282c%29%2B2b-2a ALIGN=MIDDLE  ALT=\"-4-cross%282c%29%2B4b-8a=-8-cross%282c%29%2B2b-2a\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> so,this proves that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c ALIGN=MIDDLE  ALT=\"+c\"   DISABLED_style= \"max-width:90%; height:auto;\" > can have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=any+ ALIGN=MIDDLE  ALT=\"any+\"   DISABLED_style= \"max-width:90%; height:auto;\" >value\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2B4b-8a=-8%2B2b-2a ALIGN=MIDDLE  ALT=\"-4%2B4b-8a=-8%2B2b-2a\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4b-2b=8a-8%2B4-2a ALIGN=MIDDLE  ALT=\"4b-2b=8a-8%2B4-2a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b=6a-4 ALIGN=MIDDLE  ALT=\"2b=6a-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=3a-2 ALIGN=MIDDLE  ALT=\"b=3a-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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