document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1169888>Question 1169888</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The polynomial of degree 4, P(x) has a root multiplicity 2 at x=4 and roots multiplicity 1 at x=0 and x=-1 and it goes through the point (5, 24). <BR>\n" );
document.write( "Find a formula for P(x).\r<BR>\n" );
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document.write( "P(x)= </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #794727 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</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=794727\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "given:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=x%5B2%5D=4 ALIGN=MIDDLE  ALT=\"x%5B1%5D=x%5B2%5D=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B3%5D=0 ALIGN=MIDDLE  ALT=\"x%5B3%5D=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B4%5D=-1 ALIGN=MIDDLE  ALT=\"x%5B4%5D=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and it goes through the point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24 ALIGN=MIDDLE  ALT=\"24\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=a%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29%28x-x%5B4%5D%29 ALIGN=MIDDLE  ALT=\"P%28x%29=a%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29%28x-x%5B4%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=a%28x-4%29%28x-4%29%28x-0%29%28x-%28-1%29%29 ALIGN=MIDDLE  ALT=\"P%28x%29=a%28x-4%29%28x-4%29%28x-0%29%28x-%28-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=a%28x-4%29%28x-4%29%28x%29%28x%2B1%29 ALIGN=MIDDLE  ALT=\"P%28x%29=a%28x-4%29%28x-4%29%28x%29%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=a%28x%5E2+-+8x+%2B+16%29%28x%5E2%2Bx%29 ALIGN=MIDDLE  ALT=\"P%28x%29=a%28x%5E2+-+8x+%2B+16%29%28x%5E2%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=a%28x%5E4+-+7x%5E3+%2B+8x%5E2+%2B+16x%29 ALIGN=MIDDLE  ALT=\"P%28x%29=a%28x%5E4+-+7x%5E3+%2B+8x%5E2+%2B+16x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....use given point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24 ALIGN=MIDDLE  ALT=\"24\"   DISABLED_style= \"max-width:90%; height:auto;\" >) to calculate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24=a%285%5E4+-+7%2A5%5E3+%2B+8%2A5%5E2+%2B+16%2A5%29 ALIGN=MIDDLE  ALT=\"24=a%285%5E4+-+7%2A5%5E3+%2B+8%2A5%5E2+%2B+16%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24=a%2830%29 ALIGN=MIDDLE  ALT=\"24=a%2830%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=24%2F30 ALIGN=MIDDLE  ALT=\"a=24%2F30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=4%2F5 ALIGN=MIDDLE  ALT=\"a=4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=%284%2F5%29%28x%5E4+-+7x%5E3+%2B+8x%5E2+%2B+16x%29 ALIGN=MIDDLE  ALT=\"P%28x%29=%284%2F5%29%28x%5E4+-+7x%5E3+%2B+8x%5E2+%2B+16x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=%284x%5E4%29%2F5+-%2828x%5E3%29%2F5+%2B%2832x%5E2%29%2F5+%2B%2864x%29%2F5 ALIGN=MIDDLE  ALT=\"P%28x%29=%284x%5E4%29%2F5+-%2828x%5E3%29%2F5+%2B%2832x%5E2%29%2F5+%2B%2864x%29%2F5\"   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=+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%284x%5E4%29%2F5+-%2828x%5E3%29%2F5+%2B%2832x%5E2%29%2F5+%2B%2864x%29%2F5%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );