document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200280>Question 1200280</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at x=1 and x=0, and a root of multiplicity 1 at x=−3<BR>\n" );
document.write( "Find a possible formula for P(x).<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #834376 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=834376\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "<font color=red>Answer:</font> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=+x%5E2%28x-1%29%5E2%28x%2B3%29 ALIGN=MIDDLE  ALT=\"P%28x%29+=+x%5E2%28x-1%29%5E2%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Explanation:<BR>\n" );
document.write( "If k is a root of P(x), then x-k is a factor of P(x)<BR>\n" );
document.write( "The multiplicity is the exponent for the factor.<BR>\n" );
document.write( "So that's how for instance a root of x = 1 with multiplicity 2 leads to the factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%5E2 ALIGN=MIDDLE  ALT=\"%28x-1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The leading coefficient is the number out front of the variables.<BR>\n" );
document.write( "For example, if the leading coefficient was 5, then we would have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=+5x%5E2%28x-1%29%5E2%28x%2B3%29 ALIGN=MIDDLE  ALT=\"P%28x%29+=+5x%5E2%28x-1%29%5E2%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Instead, the leading coefficient is 1 so we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=+1x%5E2%28x-1%29%5E2%28x%2B3%29 ALIGN=MIDDLE  ALT=\"P%28x%29+=+1x%5E2%28x-1%29%5E2%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > aka <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=+x%5E2%28x-1%29%5E2%28x%2B3%29 ALIGN=MIDDLE  ALT=\"P%28x%29+=+x%5E2%28x-1%29%5E2%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Optionally you can expand everything out to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=+x%5E2%28x-1%29%5E2%28x%2B3%29+=+x%5E5%2Bx%5E4-5x%5E3%2B3x%5E2 ALIGN=MIDDLE  ALT=\"P%28x%29+=+x%5E2%28x-1%29%5E2%28x%2B3%29+=+x%5E5%2Bx%5E4-5x%5E3%2B3x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "However, I don't recommend doing this since it's unnecessary and you lose the information about the roots along with their multiplicities.<BR>\n" );
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