document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1183387>Question 1183387</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The expression 8x^3 + ax^2 + bx - 9 leaves remainders -95 and 3 when divided by x + 2 and 2x - 3 respectively. Calculate the value of a and of b. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #813684 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=813684\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "given:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+8x%5E3+%2B+ax%5E2+%2B+bx+-+9 ALIGN=MIDDLE  ALT=\"+8x%5E3+%2B+ax%5E2+%2B+bx+-+9\"   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=x+%2B+2 ALIGN=MIDDLE  ALT=\"x+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a factor of given polynomial<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+2+=+0 ALIGN=MIDDLE  ALT=\"x+%2B+2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <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;\" >\r<BR>\n" );
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document.write( "Remainder = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-95 ALIGN=MIDDLE  ALT=\"-95\"   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=2x+-+3 ALIGN=MIDDLE  ALT=\"2x+-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a factor of given polynomial\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+-+3=0 ALIGN=MIDDLE  ALT=\"2x+-+3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+=3 ALIGN=MIDDLE  ALT=\"2x+=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=3%2F2 ALIGN=MIDDLE  ALT=\"x=3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Remainder =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   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=8x%5E3+%2B+ax%5E2+%2B+bx+-+9+ ALIGN=MIDDLE  ALT=\"8x%5E3+%2B+ax%5E2+%2B+bx+-+9+\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........Put the value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   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=8%28-2%29%5E3+%2B+a%28-2%29%5E2+%2B+b%28-2%29+-+9=-95 ALIGN=MIDDLE  ALT=\"8%28-2%29%5E3+%2B+a%28-2%29%5E2+%2B+b%28-2%29+-+9=-95\"   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=a%28-2%29%5E2+-+2+b+-+73+=+-95 ALIGN=MIDDLE  ALT=\"a%28-2%29%5E2+-+2+b+-+73+=+-95\"   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=4a+-2b++=-95%2B73 ALIGN=MIDDLE  ALT=\"4a+-2b++=-95%2B73\"   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=4a+++=2b-22 ALIGN=MIDDLE  ALT=\"4a+++=2b-22\"   DISABLED_style= \"max-width:90%; height:auto;\" >...........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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=2b%2F4+-22%2F4 ALIGN=MIDDLE  ALT=\"a+=2b%2F4+-22%2F4\"   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=a+=b%2F2++-11%2F2 ALIGN=MIDDLE  ALT=\"a+=b%2F2++-11%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >...........eq.1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%283%2F2%29%5E3+%2B+a%283%2F2%29%5E2+%2B+b%283%2F2%29+-+9=3 ALIGN=MIDDLE  ALT=\"8%283%2F2%29%5E3+%2B+a%283%2F2%29%5E2+%2B+b%283%2F2%29+-+9=3\"   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=8%2827%2F8%29+%2B+a%289%2F4%29+%2B+b%283%2F2%29+=3%2B9 ALIGN=MIDDLE  ALT=\"8%2827%2F8%29+%2B+a%289%2F4%29+%2B+b%283%2F2%29+=3%2B9\"   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=27+%2B+a%289%2F4%29+%2B+b%283%2F2%29+=12 ALIGN=MIDDLE  ALT=\"27+%2B+a%289%2F4%29+%2B+b%283%2F2%29+=12\"   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=a%289%2F4%29+%2B+b%283%2F2%29++=12-27 ALIGN=MIDDLE  ALT=\"a%289%2F4%29+%2B+b%283%2F2%29++=12-27\"   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=a%289%2F4%29+%2B+b%283%2F2%29++=-15 ALIGN=MIDDLE  ALT=\"a%289%2F4%29+%2B+b%283%2F2%29++=-15\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......both sides multiply by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"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=9a+%2B+6b+=-60 ALIGN=MIDDLE  ALT=\"9a+%2B+6b+=-60\"   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=3a+%2B+2b+=-20 ALIGN=MIDDLE  ALT=\"3a+%2B+2b+=-20\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a=-20-2b ALIGN=MIDDLE  ALT=\"3a=-20-2b\"   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=a=-20%2F3-2b%2F3 ALIGN=MIDDLE  ALT=\"a=-20%2F3-2b%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >...........eq.2\r<BR>\n" );
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document.write( "from eq.1 and eq.2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2F2++-11%2F2=-20%2F3-2b%2F3 ALIGN=MIDDLE  ALT=\"b%2F2++-11%2F2=-20%2F3-2b%2F3\"   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=b%2F2+%2B+2b%2F3=11%2F2-20%2F3 ALIGN=MIDDLE  ALT=\"b%2F2+%2B+2b%2F3=11%2F2-20%2F3\"   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=%287%2F6%29b=-7%2F6 ALIGN=MIDDLE  ALT=\"%287%2F6%29b=-7%2F6\"   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++=-1 ALIGN=MIDDLE  ALT=\"b++=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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=a+=b%2F2++-11%2F2 ALIGN=MIDDLE  ALT=\"a+=b%2F2++-11%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >...........eq.1, substitute<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=a+=%28-1%29%2F2++-11%2F2 ALIGN=MIDDLE  ALT=\"a+=%28-1%29%2F2++-11%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >...........eq.1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=-6 ALIGN=MIDDLE  ALT=\"a+=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then your expression is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%5E3+-6x%5E2+-x+-+9 ALIGN=MIDDLE  ALT=\"8x%5E3+-6x%5E2+-x+-+9\"   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=%288x%5E3+-6x%5E2+-x+-+9%29%2F%28x%2B2%29=8x%5E2+-+22+x+%2B+43-95%2F%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%288x%5E3+-6x%5E2+-x+-+9%29%2F%28x%2B2%29=8x%5E2+-+22+x+%2B+43-95%2F%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=8x%5E3+-+6+x%5E2+-+x+-+9+=+%28%288+x%5E2+-+22+x+%2B+43%29%29%2A%28x+%2B+2%29++-95 ALIGN=MIDDLE  ALT=\"8x%5E3+-+6+x%5E2+-+x+-+9+=+%28%288+x%5E2+-+22+x+%2B+43%29%29%2A%28x+%2B+2%29++-95\"   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=%288x%5E3+-6x%5E2+-x+-+9%29%2F%282x-3%29=4+x%5E2+%2B+3+x+%2B+4%2B3%2F%282x+-+3%29 ALIGN=MIDDLE  ALT=\"%288x%5E3+-6x%5E2+-x+-+9%29%2F%282x-3%29=4+x%5E2+%2B+3+x+%2B+4%2B3%2F%282x+-+3%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=8+x%5E3+-+6+x%5E2+-+x+-+9+=+%28%284+x%5E2+%2B+3+x+%2B+4%29%29%2A%282+x+-+3%29+%2B+3 ALIGN=MIDDLE  ALT=\"8+x%5E3+-+6+x%5E2+-+x+-+9+=+%28%284+x%5E2+%2B+3+x+%2B+4%29%29%2A%282+x+-+3%29+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );