document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1149382>Question 1149382</A>: <I><SPAN STYLE=\"word-break: break-all;\"> To Whom it May Concern,\r<BR>\n" );
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document.write( "Could you help me with this question:<BR>\n" );
document.write( "Find the quadratic which has a remainder of -6 when divided by x - 1, a<BR>\n" );
document.write( "remainder of -4 when divided by x -3 and no remainder when 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 #770714 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=770714\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"f%28x%29+=+ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Use the remainder theorem:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29%2F%28x-1%29+=+-6 ALIGN=MIDDLE  ALT=\"f%28x%29%2F%28x-1%29+=+-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29+=+-6 ALIGN=MIDDLE  ALT=\"f%281%29+=+-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb%2Bc+=+-6 ALIGN=MIDDLE  ALT=\"a%2Bb%2Bc+=+-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > (1)<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29%2F%28x-3%29+=+-4 ALIGN=MIDDLE  ALT=\"f%28x%29%2F%28x-3%29+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%283%29+=+-4 ALIGN=MIDDLE  ALT=\"f%283%29+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9a%2B3b%2Bc+=+-4 ALIGN=MIDDLE  ALT=\"9a%2B3b%2Bc+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > (2)<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29%2F%28x%2B1%29+=+0 ALIGN=MIDDLE  ALT=\"f%28x%29%2F%28x%2B1%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-1%29+=+0 ALIGN=MIDDLE  ALT=\"f%28-1%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a-b%2Bc+=+0 ALIGN=MIDDLE  ALT=\"a-b%2Bc+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (3)<br><BR>\n" );
document.write( "That gives you 3 equations in 3 unknowns; solve by any method you like.<br><BR>\n" );
document.write( "A good start might be subtracting (3) from (1); that eliminates both a and c, giving you an equation that is easily solved to find the value of b.<br><BR>\n" );
document.write( "Then substitute that value of b in (1) and (2) and solve the resulting pair of equations for a and c.<br><BR>\n" );
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