document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187763>Question 1187763</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given that f(x)=x^3+ax^2+bx-3 leaves remainders 1 and -9 when divided by x-1 and x+1. Calculate the values of a and b<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #818774 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=818774\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "use long division\r<BR>\n" );
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document.write( "......(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%28a+%2B1%29x%2B%28b%2Ba+%2B1%29 ALIGN=MIDDLE  ALT=\"x%5E2%2B%28a+%2B1%29x%2B%28b%2Ba+%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1 ALIGN=MIDDLE  ALT=\"x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >| <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2Bax%5E2%2Bbx-3 ALIGN=MIDDLE  ALT=\"x%5E3%2Bax%5E2%2Bbx-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "........<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3-x%5E2 ALIGN=MIDDLE  ALT=\"x%5E3-x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "..............<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bx%5E2 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "..............<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a+%2B1%29x%5E2%2Bbx ALIGN=MIDDLE  ALT=\"%28a+%2B1%29x%5E2%2Bbx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "..............<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a+%2B1%29x%5E2-%28a+%2B1%29x+ ALIGN=MIDDLE  ALT=\"%28a+%2B1%29x%5E2-%28a+%2B1%29x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "..............................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=bx%2B%28a+%2B1%29x+-3 ALIGN=MIDDLE  ALT=\"bx%2B%28a+%2B1%29x+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "................................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b%2Ba+%2B1%29x+-%28b%2Ba+%2B1%29 ALIGN=MIDDLE  ALT=\"%28b%2Ba+%2B1%29x+-%28b%2Ba+%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "........................................... <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2Bb%2Ba+%2B1 ALIGN=MIDDLE  ALT=\"-3%2Bb%2Ba+%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "........................................... <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b%2Ba+-2+ ALIGN=MIDDLE  ALT=\"+b%2Ba+-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> reminder<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b%2Ba+-2+=1 ALIGN=MIDDLE  ALT=\"+b%2Ba+-2+=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2Ba+=3 ALIGN=MIDDLE  ALT=\"b%2Ba+=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........eq.1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "......(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%281+-a%29x%2B%28b%2B1+-a%29 ALIGN=MIDDLE  ALT=\"x%5E2%2B%281+-a%29x%2B%28b%2B1+-a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1 ALIGN=MIDDLE  ALT=\"x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >| <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2Bax%5E2%2Bbx-3 ALIGN=MIDDLE  ALT=\"x%5E3%2Bax%5E2%2Bbx-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "........<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2Bx%5E2 ALIGN=MIDDLE  ALT=\"x%5E3%2Bx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "..............<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2-x%5E2 ALIGN=MIDDLE  ALT=\"ax%5E2-x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "...............<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281+-a%29x%5E2%2Bbx ALIGN=MIDDLE  ALT=\"%281+-a%29x%5E2%2Bbx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "...............<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281+-a%29x%5E2-%281+-a%29x+-3 ALIGN=MIDDLE  ALT=\"%281+-a%29x%5E2-%281+-a%29x+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "..........................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=bx%2B%281+-a%29x+%2B%28b%2B1+-a%29 ALIGN=MIDDLE  ALT=\"bx%2B%281+-a%29x+%2B%28b%2B1+-a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "................................................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3-%28b%2B1+-a%29+ ALIGN=MIDDLE  ALT=\"-3-%28b%2B1+-a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "................................................. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3-b-1%2Ba++ ALIGN=MIDDLE  ALT=\"-3-b-1%2Ba++\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "................................................  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a-b+-4 ALIGN=MIDDLE  ALT=\"+a-b+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > =>  reminder <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a-b+-4+=-9 ALIGN=MIDDLE  ALT=\"+a-b+-4+=-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a-b+=-5 ALIGN=MIDDLE  ALT=\"a-b+=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........eq.2\r<BR>\n" );
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document.write( "go to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2Ba+=3 ALIGN=MIDDLE  ALT=\"b%2Ba+=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........eq.1, solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=3-b ALIGN=MIDDLE  ALT=\"a=3-b\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "go to\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a-b+=-5 ALIGN=MIDDLE  ALT=\"a-b+=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........eq.2, substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3-b-b+=-5 ALIGN=MIDDLE  ALT=\"3-b-b+=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3-2b+=-5 ALIGN=MIDDLE  ALT=\"3-2b+=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2B5+=2b ALIGN=MIDDLE  ALT=\"3%2B5+=2b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b=8 ALIGN=MIDDLE  ALT=\"2b=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=4 ALIGN=MIDDLE  ALT=\"b=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=3-b ALIGN=MIDDLE  ALT=\"a=3-b\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=3-4 ALIGN=MIDDLE  ALT=\"a=3-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-1 ALIGN=MIDDLE  ALT=\"a=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "your equation is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E3-1x%5E2%2B4x-3 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E3-1x%5E2%2B4x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "check reminders:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+-+x%5E2+%2B+4+x+-+3+=+%28x%5E2+%2B+4%29%2A%28x+-+1%29+%2B+1 ALIGN=MIDDLE  ALT=\"x%5E3+-+x%5E2+%2B+4+x+-+3+=+%28x%5E2+%2B+4%29%2A%28x+-+1%29+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+-+x%5E2+%2B+4+x+-+3+=+%28x%5E2+-+2+x+%2B+6%29%2A%28x+%2B+1%29+%2B+%28-9%29 ALIGN=MIDDLE  ALT=\"x%5E3+-+x%5E2+%2B+4+x+-+3+=+%28x%5E2+-+2+x+%2B+6%29%2A%28x+%2B+1%29+%2B+%28-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );