document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1183399>Question 1183399</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The remainder when ax^3 + bx^2 + 2x + 3 is divided by x-1 is twice that when it is divided by x+1. Show that b = 3a + 3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #813698 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=813698\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+ax%5E3+%2B+bx%5E2+%2B+2x+%2B+3 ALIGN=MIDDLE  ALT=\"f%28x%29+=+ax%5E3+%2B+bx%5E2+%2B+2x+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then by the remainder theorem, the remainder upon division of <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;\" > by <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;\" > is equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29+=+a%2Bb%2B2%2B3+=+a%2Bb%2B5 ALIGN=MIDDLE  ALT=\"f%281%29+=+a%2Bb%2B2%2B3+=+a%2Bb%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Similarly, the remainder upon division of <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;\" > by <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;\" > is equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-1%29+=+-a%2Bb-2%2B3+=+-a%2Bb%2B1 ALIGN=MIDDLE  ALT=\"f%28-1%29+=+-a%2Bb-2%2B3+=+-a%2Bb%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "From the given, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29+=+2f%28-1%29 ALIGN=MIDDLE  ALT=\"f%281%29+=+2f%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, hence\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb%2B5+=+2%28-a%2Bb%2B1%29+=+-2a%2B2b%2B2 ALIGN=MIDDLE  ALT=\"a%2Bb%2B5+=+2%28-a%2Bb%2B1%29+=+-2a%2B2b%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%283a+%2B+3+=+b%29 ALIGN=MIDDLE  ALT=\"highlight%283a+%2B+3+=+b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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