document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1159546>Question 1159546</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The function f is given by f(x)=x^3+2x^2+ax-8 where a is constant.when f(x) is  divided by (x-2) the remainder is -6.<BR>\n" );
document.write( "Show that (x+1) is a factor of f(x) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #782596 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=782596\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> given:\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%2B2x%5E2%2Bax-8 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E3%2B2x%5E2%2Bax-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > is constant.when<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29 ALIGN=MIDDLE  ALT=\"+f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is divided by<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x-2%29 ALIGN=MIDDLE  ALT=\"+%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > the remainder is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6 ALIGN=MIDDLE  ALT=\"-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "first find <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=x%5E2%2B4x%2B%28a%2B8%29 ALIGN=MIDDLE  ALT=\"x%5E2%2B4x%2B%28a%2B8%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-2%29 ALIGN=MIDDLE  ALT=\"%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > |<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2B2x%5E2%2Bax-8 ALIGN=MIDDLE  ALT=\"x%5E3%2B2x%5E2%2Bax-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".........<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3-2x%5E2 ALIGN=MIDDLE  ALT=\"x%5E3-2x%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=4x%5E2%2Bax ALIGN=MIDDLE  ALT=\"4x%5E2%2Bax\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "...............<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2-8x ALIGN=MIDDLE  ALT=\"4x%5E2-8x\"   DISABLED_style= \"max-width:90%; height:auto;\" >............subtract<BR>\n" );
document.write( ".......................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%2B8x ALIGN=MIDDLE  ALT=\"ax%2B8x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......<BR>\n" );
document.write( ".......................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2B8%29x ALIGN=MIDDLE  ALT=\"%28a%2B8%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "........................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2B8%29x-8 ALIGN=MIDDLE  ALT=\"%28a%2B8%29x-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".......................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2B8%29x-2%28a%2B8%29 ALIGN=MIDDLE  ALT=\"%28a%2B8%29x-2%28a%2B8%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=-8%2B2%28a%2B8%29 ALIGN=MIDDLE  ALT=\"-8%2B2%28a%2B8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......<BR>\n" );
document.write( "..................................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8%2B2a%2B8 ALIGN=MIDDLE  ALT=\"-8%2B2a%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......<BR>\n" );
document.write( ".........................................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a ALIGN=MIDDLE  ALT=\"2a\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........reminder\r<BR>\n" );
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document.write( "if given the remainder is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6 ALIGN=MIDDLE  ALT=\"-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2a=-6+ ALIGN=MIDDLE  ALT=\"+2a=-6+\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> <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 quotient is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B4x%2B%28a%2B8%29=x%5E2%2B4x-3%2B8=x%5E2%2B4x%2B5 ALIGN=MIDDLE  ALT=\"x%5E2%2B4x%2B%28a%2B8%29=x%5E2%2B4x-3%2B8=x%5E2%2B4x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29=x%5E3%2B2x%5E2-3x-8+ ALIGN=MIDDLE  ALT=\"+f%28x%29=x%5E3%2B2x%5E2-3x-8+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=> since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+%2B+4+x+%2B+5%29%28x+-+2%29=x%5E3+%2B+2+x%5E2+-+3+x+-+10 ALIGN=MIDDLE  ALT=\"%28x%5E2+%2B+4+x+%2B+5%29%28x+-+2%29=x%5E3+%2B+2+x%5E2+-+3+x+-+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "subtract it from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2B2x%5E2-3x-8 ALIGN=MIDDLE  ALT=\"x%5E3%2B2x%5E2-3x-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >  to find new reminder\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2B2x%5E2-3x-8-%28x%5E3+%2B+2+x%5E2+-+3+x+-+10%29=x%5E3%2B2x%5E2-3x-8-x%5E3+-2+x%5E2+%2B3+x+%2B+10=2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=> reminder is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2B2x%5E2-3x-8+=%28x%5E2+%2B+4+x+%2B+5%29%28x+-+2%29%2B2 ALIGN=MIDDLE  ALT=\"x%5E3%2B2x%5E2-3x-8+=%28x%5E2+%2B+4+x+%2B+5%29%28x+-+2%29%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "also given that:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29 ALIGN=MIDDLE  ALT=\"+f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be written in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29%28x%5E2%2Bbx%2Bc%29 ALIGN=MIDDLE  ALT=\"%28x%2B1%29%28x%5E2%2Bbx%2Bc%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+ ALIGN=MIDDLE  ALT=\"+b+\"   DISABLED_style= \"max-width:90%; height:auto;\" >and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" > are constants\r<BR>\n" );
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document.write( "find the values of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   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=+f%28x%29=x%5E3%2B2x%5E2-3x-8+ ALIGN=MIDDLE  ALT=\"+f%28x%29=x%5E3%2B2x%5E2-3x-8+\"   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%2B2x%5E2-3x-8=%28x%2B1%29%28x%5E2%2Bbx%2Bc%29+ ALIGN=MIDDLE  ALT=\"+x%5E3%2B2x%5E2-3x-8=%28x%2B1%29%28x%5E2%2Bbx%2Bc%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....expand right side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E3%2B2x%5E2-3x-8=bx%5E2+%2B+bx+%2B+cx+%2B+c+%2B+x%5E3+%2B+x%5E2 ALIGN=MIDDLE  ALT=\"+x%5E3%2B2x%5E2-3x-8=bx%5E2+%2B+bx+%2B+cx+%2B+c+%2B+x%5E3+%2B+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=+x%5E3%2B2x%5E2-3x-8=x%5E3%2B+x%5E2%2B+bx%5E2+%2B+bx+%2B+cx+%2B+c++ ALIGN=MIDDLE  ALT=\"+x%5E3%2B2x%5E2-3x-8=x%5E3%2B+x%5E2%2B+bx%5E2+%2B+bx+%2B+cx+%2B+c++\"   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%5E3%2B2x%5E2-3x-8=x%5E3%2B+%281%2B+b%29x%5E2+%2B+%28b+%2B+c%29x+%2B+c++ ALIGN=MIDDLE  ALT=\"+x%5E3%2B2x%5E2-3x-8=x%5E3%2B+%281%2B+b%29x%5E2+%2B+%28b+%2B+c%29x+%2B+c++\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....compare coefficients\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2=%281%2B+b%29 ALIGN=MIDDLE  ALT=\"2=%281%2B+b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=2-1 ALIGN=MIDDLE  ALT=\"b=2-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b+%2B+c%29=-3 ALIGN=MIDDLE  ALT=\"%28b+%2B+c%29=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Bc=-3 ALIGN=MIDDLE  ALT=\"1%2Bc=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-4 ALIGN=MIDDLE  ALT=\"c=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "substitute in\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2B+%281%2B+b%29x%5E2+%2B+%28b+%2B+c%29x+%2B+c++ ALIGN=MIDDLE  ALT=\"x%5E3%2B+%281%2B+b%29x%5E2+%2B+%28b+%2B+c%29x+%2B+c++\"   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%5E3%2B+%281%2B+1%29x%5E2+%2B+%281+-4%29x+-4++ ALIGN=MIDDLE  ALT=\"+x%5E3%2B+%281%2B+1%29x%5E2+%2B+%281+-4%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=+x%5E3%2B+2x%5E2+%2B++-3x+-4++ ALIGN=MIDDLE  ALT=\"+x%5E3%2B+2x%5E2+%2B++-3x+-4++\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "subtract \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+%2B+2+x%5E2+-+3+x+-+8+-+%28x%5E3+%2B+2+x%5E2+-+3+x+-+4%29=x%5E3+%2B+2+x%5E2+-+3+x+-+8-+x%5E3+-+2+x%5E2+%2B3+x+%2B+4=-4 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, new reminder is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-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=x%5E3+%2B+2+x%5E2+-+3+x+-+8+=+%28x%5E2+%2B+x+-+4%29+%28x+%2B+1%29++-4 ALIGN=MIDDLE  ALT=\"x%5E3+%2B+2+x%5E2+-+3+x+-+8+=+%28x%5E2+%2B+x+-+4%29+%28x+%2B+1%29++-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );