document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=925979>Question 925979</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if P^3+3P^2+3P=7, then the value of P^2+2P is </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #561895 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=561895\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The requested expression may have more than just one possible value, but at least this analysis works:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5E3%2B3p%5E2%2B3p-7=0 ALIGN=MIDDLE  ALT=\"p%5E3%2B3p%5E2%2B3p-7=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and testing of roots using Rational Roots Theorem and synthetic division shows....\r<BR>\n" );
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document.write( "_______1_____|_______1______3_______3______-7<BR>\n" );
document.write( "_____________|<BR>\n" );
document.write( "_____________|<BR>\n" );
document.write( "_____________|_____________1_______4________7<BR>\n" );
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document.write( "____________________1______4_______7_________0\r<BR>\n" );
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document.write( "Note the remainder  of  0.<BR>\n" );
document.write( "The equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28p-1%29%28p%5E2%2B4p%2B7%29=0 ALIGN=MIDDLE  ALT=\"%28p-1%29%28p%5E2%2B4p%2B7%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, with the found solution p=1.\r<BR>\n" );
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document.write( "You can use this to get a value for the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5E2%2B2p ALIGN=MIDDLE  ALT=\"p%5E2%2B2p\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%5E2%2B2%2A1 ALIGN=MIDDLE  ALT=\"1%5E2%2B2%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%283%29 ALIGN=MIDDLE  ALT=\"highlight%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "No other real value for p.<BR>\n" );
document.write( "The quadratic factor is not factorable in real numbers.<BR>\n" );
document.write( "(Discriminant is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A4-4%2A7=16-28=-12%3C0 ALIGN=MIDDLE  ALT=\"4%2A4-4%2A7=16-28=-12%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" > .) </SPAN>\n" );
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