document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1154891>Question 1154891</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find a polynomial of degree 3 such that when divided by x^2-5x has a remainder of<BR>\n" );
document.write( "6x-15 and when divided by x^2-5x+8 has a remainder of 2x-7. <BR>\n" );
document.write( "Please explain as well.<BR>\n" );
document.write( "Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #777420 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=777420\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Find a polynomial of degree <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > such that when divided by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-5x ALIGN=MIDDLE  ALT=\"x%5E2-5x\"   DISABLED_style= \"max-width:90%; height:auto;\" > has a remainder of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x-15 ALIGN=MIDDLE  ALT=\"6x-15\"   DISABLED_style= \"max-width:90%; height:auto;\" > and when divided by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-5x%2B8 ALIGN=MIDDLE  ALT=\"x%5E2-5x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > has a remainder of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-7 ALIGN=MIDDLE  ALT=\"2x-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29%2Fg%28x%29=q%28x%29%2Breminder ALIGN=MIDDLE  ALT=\"f%28x%29%2Fg%28x%29=q%28x%29%2Breminder\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=q%28x%29%2Ag%28x%29%2Breminder ALIGN=MIDDLE  ALT=\"f%28x%29=q%28x%29%2Ag%28x%29%2Breminder\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if given <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=+x%5E2-5x ALIGN=MIDDLE  ALT=\"g%28x%29=+x%5E2-5x\"   DISABLED_style= \"max-width:90%; height:auto;\" >  and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=reminder+=6x-15 ALIGN=MIDDLE  ALT=\"reminder+=6x-15\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=q%28x%29%2A%28x%5E2-5x+%29%2B6x-15 ALIGN=MIDDLE  ALT=\"f%28x%29=q%28x%29%2A%28x%5E2-5x+%29%2B6x-15\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......eq.1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "and  if given <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=+x%5E2-5x%2B8 ALIGN=MIDDLE  ALT=\"g%28x%29=+x%5E2-5x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" >  and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=reminder+=2x-7 ALIGN=MIDDLE  ALT=\"reminder+=2x-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=q%28x%29%2A%28x%5E2-5x%2B8%29%2B2x-7 ALIGN=MIDDLE  ALT=\"f%28x%29=q%28x%29%2A%28x%5E2-5x%2B8%29%2B2x-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......eq.2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "from eq.1 and eq.2 we have\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q%28x%29%2A%28x%5E2-5x+%29%2B6x-15=q%28x%29%2A%28x%5E2-5x%2B8%29%2B2x-7 ALIGN=MIDDLE  ALT=\"q%28x%29%2A%28x%5E2-5x+%29%2B6x-15=q%28x%29%2A%28x%5E2-5x%2B8%29%2B2x-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q%28x%29%2A%28x%5E2-5x+%29-q%28x%29%2A%28x%5E2-5x%2B8%29=2x-6x%2B15-7 ALIGN=MIDDLE  ALT=\"q%28x%29%2A%28x%5E2-5x+%29-q%28x%29%2A%28x%5E2-5x%2B8%29=2x-6x%2B15-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q%28x%29 ALIGN=MIDDLE  ALT=\"q%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q%28x%29%28x%5E2-5x+-%28x%5E2-5x%2B8%29%29=-4x%2B8 ALIGN=MIDDLE  ALT=\"q%28x%29%28x%5E2-5x+-%28x%5E2-5x%2B8%29%29=-4x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q%28x%29%28x%5E2-5x+-x%5E2%2B5x-8%29=-4x%2B8 ALIGN=MIDDLE  ALT=\"q%28x%29%28x%5E2-5x+-x%5E2%2B5x-8%29=-4x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......simplify\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q%28x%29%28-8%29=-4x%2B8 ALIGN=MIDDLE  ALT=\"q%28x%29%28-8%29=-4x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q%28x%29=-4x%2F%28-8%29%2B8%2F%28-8%29 ALIGN=MIDDLE  ALT=\"q%28x%29=-4x%2F%28-8%29%2B8%2F%28-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q%28x%29=x%2F2-1 ALIGN=MIDDLE  ALT=\"q%28x%29=x%2F2-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> your quotient\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "now find <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;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=q%28x%29%2Ag%28x%29%2Breminder ALIGN=MIDDLE  ALT=\"f%28x%29=q%28x%29%2Ag%28x%29%2Breminder\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x%2F2-1%29%2A%28x%5E2-5x+%29%2B6x-15 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%2F2-1%29%2A%28x%5E2-5x+%29%2B6x-15\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......eq.1\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E3%2F2-5x%5E2%2F2-x%5E2+%2B5x%2B6x-15 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E3%2F2-5x%5E2%2F2-x%5E2+%2B5x%2B6x-15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E3%2F2+-+7x%5E2%2F2+%2B11x+-+15 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E3%2F2+-+7x%5E2%2F2+%2B11x+-+15\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> your polynomial of degree <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );