document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1053225>Question 1053225</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use polynomial division to find the quotient Q(x) and the remainder R(x) when the first polynomial is divided by the second polynomial.\r<BR>\n" );
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document.write( "1.   X^4-x^3+2x^2-x+1,  x^2+1\r<BR>\n" );
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document.write( "2.    X^5+32,x-2\r<BR>\n" );
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document.write( "3.     6x^4-x^2+4, x-3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #668505 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=668505\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x^4-x^3+2x^2-x+1 by x^2+1\r<BR>\n" );
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document.write( "=======x^2+x+1<BR>\n" );
document.write( "x^2+1/x^4+x^3+2x^2-x+1<BR>\n" );
document.write( "======x^4+=====x^2<BR>\n" );
document.write( "subtract===x^3+x^2-x+1<BR>\n" );
document.write( "===========x^3+====-x<BR>\n" );
document.write( "subtract=======x^2-2x+1<BR>\n" );
document.write( "===============x^2+1<BR>\n" );
document.write( "subtract, and remainder -2x. Q(x)=x^2+x+1, R(x)=-2x<BR>\n" );
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document.write( "x^5+32 by x-2-------------------------------------\r<BR>\n" );
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document.write( "=====x^4+2x^3+4x^2+8x+16<BR>\n" );
document.write( "x-2/x^5+0x^4+0x^3+0x^2+0x+32<BR>\n" );
document.write( "====x^5-2x4<BR>\n" );
document.write( "subtract 2x^4+============32<BR>\n" );
document.write( "=========2x^4-4x^3<BR>\n" );
document.write( "subtract======-4x^3========32<BR>\n" );
document.write( "===============4x^3-8x^2<BR>\n" );
document.write( "subtract=============8x^2+32<BR>\n" );
document.write( "=====================8x^2-16x<BR>\n" );
document.write( "subtract===================+16x+32<BR>\n" );
document.write( "===========================-16x+32<BR>\n" );
document.write( "subtract====================0  Q(x)=x^4+2x^3+4x^2+8x+16, R(x)=0<BR>\n" );
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document.write( "======6x^3+18x^2+53x+159<BR>\n" );
document.write( "x-3/6x^4+0x^3-x^2+0x+4<BR>\n" );
document.write( "====6x^4-18x^3<BR>\n" );
document.write( "subtract 18x^3-x^2+4<BR>\n" );
document.write( "========18x^3-54x^2<BR>\n" );
document.write( "subtract======53x^2+0x+4<BR>\n" );
document.write( "==============53x^2-159x<BR>\n" );
document.write( "subtract===========159x+4<BR>\n" );
document.write( "===================159x-477<BR>\n" );
document.write( "subtract================+481 Q(x)=6x^3+18x^2+53x+159. R(x)=481\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );