document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=320799>Question 320799</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How can i use the rational root theorem and polynomail long division to factor the following completely? x^3+3x^2+3x+1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #229696 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=229696\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> From the rational roots theorem, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=0+%2B-+1 ALIGN=MIDDLE  ALT=\"p=0+%2B-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29=1%2B3%2B3%2B1=8 ALIGN=MIDDLE  ALT=\"f%281%29=1%2B3%2B3%2B1=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1 ALIGN=MIDDLE  ALT=\"x=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-1%29=-1%2B3-3%2B1=0 ALIGN=MIDDLE  ALT=\"f%28-1%29=-1%2B3-3%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1 ALIGN=MIDDLE  ALT=\"x=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a root and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1 ALIGN=MIDDLE  ALT=\"x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a factor of the polynomial.<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now use polynomial long division to find the remaining quadratic,<BR>\n" );
document.write( "First term: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28+x%5E2%29 ALIGN=MIDDLE  ALT=\"highlight%28+x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%28x%2B1%29=x%5E3%2Bx%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%28x%2B1%29=x%5E3%2Bx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract that product from the original polynomial to get the remainder,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E3%2B3x%5E2%2B3x%2B1%29-%28x%5E3%2Bx%5E2%29=2x%5E2%2B3x%2B1 ALIGN=MIDDLE  ALT=\"%28x%5E3%2B3x%5E2%2B3x%2B1%29-%28x%5E3%2Bx%5E2%29=2x%5E2%2B3x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Second term:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%282x%29 ALIGN=MIDDLE  ALT=\"highlight%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%28x%2B1%29=2x%5E2%2B2x ALIGN=MIDDLE  ALT=\"2x%28x%2B1%29=2x%5E2%2B2x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract that product from the previous remainder to get the new remainder,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%5E2%2B3x%2B1%29-%282x%5E2%2B2x%29=x%2B1 ALIGN=MIDDLE  ALT=\"%282x%5E2%2B3x%2B1%29-%282x%5E2%2B2x%29=x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Final term:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%281%29 ALIGN=MIDDLE  ALT=\"highlight%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%28x%2B1%29=x%2B1 ALIGN=MIDDLE  ALT=\"1%28x%2B1%29=x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract that product from the previous remainder to get the new remainder,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B1%29-%28x%2B1%29=0 ALIGN=MIDDLE  ALT=\"%28x%2B1%29-%28x%2B1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Gather all of the terms.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E3%2B3x%5E2%2B3x%2B1%29%2F%28x%2B1%29=x%5E2%2B2x%2B1=%28x%2B1%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%5E3%2B3x%5E2%2B3x%2B1%29%2F%28x%2B1%29=x%5E2%2B2x%2B1=%28x%2B1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2B3x%5E2%2B3x%2B1=%28x%2B1%29%5E3 ALIGN=MIDDLE  ALT=\"x%5E3%2B3x%5E2%2B3x%2B1=%28x%2B1%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "A triple root at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1 ALIGN=MIDDLE  ALT=\"x=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );