document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=443086>Question 443086</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having trouble with this homework problem, I'm not sure what to do could you please help me:<BR>\n" );
document.write( "Use the polynomial that defines P as the dividend and the binomial that defines D as the divisor. Write the division in the form P(x)=D(x) x Q(x)+R where the polynomial that defines Q is the quotient and R is an integar remainder for the equation P(x)=2x^3-5x^2+8x-5; D(x)= 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 #305624 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><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=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=305624\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is just a fancy way of them saying: DO LONG DIVISION. Then take your solution and multiply it by your dividend to get your original polynomial. So let's do it:\r<BR>\n" );
document.write( "\n" );
document.write( "x-1 |  2x^3 -5x^2 + 8x -5\r<BR>\n" );
document.write( "\n" );
document.write( "How many times does x go into 2x^3?  2x^2 times.\r<BR>\n" );
document.write( "\n" );
document.write( "(x-1)*2x^2 = 2x^3 +2x^2\r<BR>\n" );
document.write( "\n" );
document.write( "2x^3 -5x^2 + 8x -5<BR>\n" );
document.write( "-(2x^3 -2x^2 +0 + 0)<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( " 0  -3x^2 + 8x - 5\r<BR>\n" );
document.write( "\n" );
document.write( "How many times does x go into  -3x^2?  -3x times.\r<BR>\n" );
document.write( "\n" );
document.write( "(x-1)*(-3x) = -3x^2 + 3x\r<BR>\n" );
document.write( "\n" );
document.write( "-3x^2 +8x 0 -5<BR>\n" );
document.write( "-(-3x^2 + 3x +0)<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "   0   +5x - 5\r<BR>\n" );
document.write( "\n" );
document.write( "How many times does x go into 5x?  5 times.\r<BR>\n" );
document.write( "\n" );
document.write( "(x-1)*5 = 5x -5\r<BR>\n" );
document.write( "\n" );
document.write( "5x-5<BR>\n" );
document.write( "-(5x-5)<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "0<BR>\n" );
document.write( "---------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So we have our Q(x) + R = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%5E2+-3x+%2B+5%29%2A%28x-1%29 ALIGN=MIDDLE  ALT=\"%282x%5E2+-3x+%2B+5%29%2A%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "So then,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%282x%5E3+-5x%5E2+%2B+8++=++%282x%5E2-3x%2B5%29%2A%28x-1%29%29 ALIGN=MIDDLE  ALT=\"highlight%282x%5E3+-5x%5E2+%2B+8++=++%282x%5E2-3x%2B5%29%2A%28x-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "Let's check this\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E3+-+3x%5E2+%2B5x+-2x%5E2+%2B3x+-5+=+2x%5E3+-5x%5E2+%2B8x+-5 ALIGN=MIDDLE  ALT=\"2x%5E3+-+3x%5E2+%2B5x+-2x%5E2+%2B3x+-5+=+2x%5E3+-5x%5E2+%2B8x+-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Check.\r<BR>\n" );
document.write( "\n" );
document.write( "So then our representation is correct.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );