document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=696139>Question 696139</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the identity Ax^3+x^2-2x-3=(3x+B)(x-1)(x+2)+C(x-1)+D , find the values of the constants A,B,C and D. Hence or otherwise, find the remainder when Ax^3+x^2-2x-3 is divided by x–1. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #428938 by </B><A HREF=/tutors/aboutme.mpl?userid=MathTherapy><B>MathTherapy(10556)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathTherapy><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=MathTherapy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=428938\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given the identity Ax^3+x^2-2x-3=(3x+B)(x-1)(x+2)+C(x-1)+D , find the values of the constants A,B,C and D. Hence or otherwise, find the remainder when Ax^3+x^2-2x-3 is divided by x–1.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x+%2B+B%29%28x+-+1%29%28x+%2B+2%29+%2B+C%28x+-+1%29+%2B+D+=+Ax%5E3+%2B+x%5E2+-+2x+-+3 ALIGN=MIDDLE  ALT=\"%283x+%2B+B%29%28x+-+1%29%28x+%2B+2%29+%2B+C%28x+-+1%29+%2B+D+=+Ax%5E3+%2B+x%5E2+-+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=%283x+%2B+B%29%28x%5E2+%2B+x+-+2%29+%2B+C%28x+-+1%29+%2B+D+=+Ax%5E3+%2B+x%5E2+-+2x+-+3 ALIGN=MIDDLE  ALT=\"%283x+%2B+B%29%28x%5E2+%2B+x+-+2%29+%2B+C%28x+-+1%29+%2B+D+=+Ax%5E3+%2B+x%5E2+-+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=3x%5E3+%2B+3x%5E2+-+6x+%2B+Bx%5E2+%2B+Bx+-+2B+%2B+Cx+-+C+%2B+D+=+Ax%5E3+%2B+x%5E2+-+2x+-+3 ALIGN=MIDDLE  ALT=\"3x%5E3+%2B+3x%5E2+-+6x+%2B+Bx%5E2+%2B+Bx+-+2B+%2B+Cx+-+C+%2B+D+=+Ax%5E3+%2B+x%5E2+-+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=3x%5E3+%2B+3x%5E2+%2B+Bx%5E2+-+6x+%2B+Bx+%2B+Cx+-+2B+-+C+%2B+D+=+Ax%5E3+%2B+x%5E2+-+2x+-+3 ALIGN=MIDDLE  ALT=\"3x%5E3+%2B+3x%5E2+%2B+Bx%5E2+-+6x+%2B+Bx+%2B+Cx+-+2B+-+C+%2B+D+=+Ax%5E3+%2B+x%5E2+-+2x+-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----- Rearranging terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%5E3%29+%2B+%283x%5E2+%2B+Bx%5E2%29+%2B+%28-+6x+%2B+Bx+%2B+Cx%29+%2B+%28-+2B+-+C+%2B+D%29+=+%28Ax%5E3%29+%2B+%28x%5E2%29+%2B++%28-+2x%29+%2B+%28+-+3%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "From the above, we can see that:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E3+=+Ax%5E3 ALIGN=MIDDLE  ALT=\"3x%5E3+=+Ax%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > -------- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%283+=+A%29 ALIGN=MIDDLE  ALT=\"highlight_green%283+=+A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2+%2B+Bx%5E2+=+x%5E2 ALIGN=MIDDLE  ALT=\"3x%5E2+%2B+Bx%5E2+=+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ------ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Bx%5E2+=+x%5E2+-+3x%5E2 ALIGN=MIDDLE  ALT=\"Bx%5E2+=+x%5E2+-+3x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ------ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Bx%5E2+=+-+2x%5E2 ALIGN=MIDDLE  ALT=\"Bx%5E2+=+-+2x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28B+=+-+2%29 ALIGN=MIDDLE  ALT=\"highlight_green%28B+=+-+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-+6x+%2B+Bx+%2B+Cx+=+-+2x ALIGN=MIDDLE  ALT=\"-+6x+%2B+Bx+%2B+Cx+=+-+2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28-+6+%2B+B+%2B+C%29+=+x%28-+2%29 ALIGN=MIDDLE  ALT=\"x%28-+6+%2B+B+%2B+C%29+=+x%28-+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-+6+%2B+B+%2B+C+=+-+2 ALIGN=MIDDLE  ALT=\"-+6+%2B+B+%2B+C+=+-+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B+%2B+C+=+4 ALIGN=MIDDLE  ALT=\"B+%2B+C+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-+2+%2B+C+=+4 ALIGN=MIDDLE  ALT=\"-+2+%2B+C+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----- Substituting – 2 for B<BR>\n" );
document.write( "C = 4 + 2, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28C+=+6%29 ALIGN=MIDDLE  ALT=\"highlight_green%28C+=+6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-+2B+-+C+%2B+D+=+-+3 ALIGN=MIDDLE  ALT=\"-+2B+-+C+%2B+D+=+-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-+2%28-+2%29+-+6+%2B+D+=+-+3 ALIGN=MIDDLE  ALT=\"-+2%28-+2%29+-+6+%2B+D+=+-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----- Substituting – 2 for B, and 6 for C<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+-+6+%2B+D+=+-+3 ALIGN=MIDDLE  ALT=\"4+-+6+%2B+D+=+-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "D = - 3 + 2, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28D+=+-+1%29 ALIGN=MIDDLE  ALT=\"highlight_green%28D+=+-+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "With <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+3 ALIGN=MIDDLE  ALT=\"A+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ax%5E3+%2B+x%5E2+-+2x+-+3 ALIGN=MIDDLE  ALT=\"Ax%5E3+%2B+x%5E2+-+2x+-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E3+%2B+x%5E2+-+2x+-+3 ALIGN=MIDDLE  ALT=\"3x%5E3+%2B+x%5E2+-+2x+-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and when divided by x – 1, we have a remainder, or f(1) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%281%29%5E3+%2B+%281%29%5E2+-+2%281%29+-+3 ALIGN=MIDDLE  ALT=\"3%281%29%5E3+%2B+%281%29%5E2+-+2%281%29+-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+%2B+1+-+2+-+3 ALIGN=MIDDLE  ALT=\"3+%2B+1+-+2+-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28-+1%29 ALIGN=MIDDLE  ALT=\"highlight_green%28-+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You can do the check!!\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Send comments and “thank-yous” to “D” at MathMadEzy@aol.com </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );