document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1147584>Question 1147584</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the quadratic which has a remainder of -6 when divided by x-1, <BR>\n" );
document.write( "a remainder of -4 when divided by x-3, and no remainder when divided<BR>\n" );
document.write( "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 #768997 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=768997\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the quadratic which has a remainder of -6 when divided by x-1, a remainder of -4 when divided by x-3, and no remainder when divided by x+1.<BR>\n" );
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document.write( "Use the form ax^2 + bx + c, we assume a=1<BR>\n" );
document.write( "Synthetic division; divisor is (x-1) remainder is -6<BR>\n" );
document.write( "....__________<BR>\n" );
document.write( " 1 | 1 + b + c<BR>\n" );
document.write( "...........1+(b+1)<BR>\n" );
document.write( "....------------<BR>\n" );
document.write( "...... 1+(b+1)- 6; the equation from this<BR>\n" );
document.write( "(b+1)+c = -6<BR>\n" );
document.write( "b + c = -7<BR>\n" );
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document.write( "divisor is (x-3) remainder is -4<BR>\n" );
document.write( "....__________<BR>\n" );
document.write( "3 | 1 + b + c<BR>\n" );
document.write( "...........3+(3b+9)<BR>\n" );
document.write( "....------------<BR>\n" );
document.write( "......1+(b+3) - 4; the equation from this<BR>\n" );
document.write( "3b+9 + c = -4<BR>\n" );
document.write( "3b + c = -4 - 9<BR>\n" );
document.write( "3b + c = -13<BR>\n" );
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document.write( "Use elimination with these two equations to find b<BR>\n" );
document.write( "3b + c = -13<BR>\n" );
document.write( " b + c = -7<BR>\n" );
document.write( "----------------subtraction eliminates c find b<BR>\n" );
document.write( "2b + 0 = -6<BR>\n" );
document.write( "b = -3<BR>\n" );
document.write( "find c when b=-3<BR>\n" );
document.write( "-3 + c = -7<BR>\n" );
document.write( "c = -7 + 3<BR>\n" );
document.write( "c = -4<BR>\n" );
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document.write( "The equation: y = x^2 - 3x - 4<BR>\n" );
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document.write( "you can confirm this:<BR>\n" );
document.write( "perform long division using divisors (x-1) and (x-3) to give remainders of  -6 and -4, respectively\r<BR>\n" );
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document.write( "  </SPAN>\n" );
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