document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=557526>Question 557526</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Another problem. Please help. My last question was nicely solved by  stanbon(47716) and I salute you. the question is:-<BR>\n" );
document.write( "When the expression a^+bx+c is divided by x-2, the remainder is R. When the expression is divided by x+1, the remainder is still R. <BR>\n" );
document.write( "  i.) Find the value of b.<BR>\n" );
document.write( " ii.) When the expression is divided by x-4, the remainder is 2R. Find the value of c and R.<BR>\n" );
document.write( "iii.) When the expression is divided by x-t, the remainder is 5R. Find the two possible values of t. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #362684 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=362684\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i.<BR>\n" );
document.write( "I suspect you mean<BR>\n" );
document.write( "\"When the expression C is divided by x-2, the remainder is R. When the expression is divided by x+1, the remainder is still R.\"<BR>\n" );
document.write( "You have a quadratic trinomial <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"P%28x%29=ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "When you divide a polynomial P(x) by (x-a), the original polynomial, P(x), the quotient polynomial, Q(x), and the remainder R, are related through:<BR>\n" );
document.write( "P(x)=Q(x)(x-a)+R (and P(a)=R).<BR>\n" );
document.write( "So,<BR>\n" );
document.write( "P(x)-R = Q(x)(x-a) is divisible by x-a.<BR>\n" );
document.write( "In the case of your polynomial, P(x)-R is divisible by x-2 and by x+1.<BR>\n" );
document.write( "So it is divisible by <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%28x%2B1%29=x%5E2-x-2 ALIGN=MIDDLE  ALT=\"%28x-2%29%28x%2B1%29=x%5E2-x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29-R=ax%5E2%2Bbx%2Bc=a%28x-2%29%28x%2B1%29=a%28x%5E2-x-2%29=ax%5E2-ax-2a ALIGN=MIDDLE  ALT=\"P%28x%29-R=ax%5E2%2Bbx%2Bc=a%28x-2%29%28x%2B1%29=a%28x%5E2-x-2%29=ax%5E2-ax-2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=a%28x-2%29%28x%2B1%29%2BR=ax%5E2-ax-2a%2BR ALIGN=MIDDLE  ALT=\"P%28x%29=a%28x-2%29%28x%2B1%29%2BR=ax%5E2-ax-2a%2BR\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-a ALIGN=MIDDLE  ALT=\"b=-a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "ii.<BR>\n" );
document.write( "P(4) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%284-2%29%284%2B1%29%2BR=10a%2BR=2R ALIGN=MIDDLE  ALT=\"a%284-2%29%284%2B1%29%2BR=10a%2BR=2R\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10a%2BR=2R ALIGN=MIDDLE  ALT=\"10a%2BR=2R\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R=10a ALIGN=MIDDLE  ALT=\"R=10a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-2a%2BR=-2a%2B10a=8a ALIGN=MIDDLE  ALT=\"c=-2a%2BR=-2a%2B10a=8a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "iii.<BR>\n" );
document.write( "P(t) =  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=at%5E2-at%2B8a ALIGN=MIDDLE  ALT=\"at%5E2-at%2B8a\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5R ALIGN=MIDDLE  ALT=\"5R\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50a ALIGN=MIDDLE  ALT=\"50a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=at%5E2-at%2B8a=50a ALIGN=MIDDLE  ALT=\"at%5E2-at%2B8a=50a\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2-t-42a=0 ALIGN=MIDDLE  ALT=\"t%5E2-t-42a=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Factoring, we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2-t-42a=%28t-7%29%28t%2B6%29 ALIGN=MIDDLE  ALT=\"t%5E2-t-42a=%28t-7%29%28t%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28t-7%29%28t%2B6%29=0 ALIGN=MIDDLE  ALT=\"%28t-7%29%28t%2B6%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > has solutions <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t-7 ALIGN=MIDDLE  ALT=\"t-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-6 ALIGN=MIDDLE  ALT=\"t=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );