document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1023589>Question 1023589</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me I am so lost. Please show all steps and work. Thanks\r<BR>\n" );
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document.write( " Real Zeros of Polynomials\r<BR>\n" );
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document.write( "The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at x=3 and x=0, and a root of multiplicity 1 at x=&#8722;4\r<BR>\n" );
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document.write( " Find a possible formula for P(x).\r<BR>\n" );
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document.write( "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 #639091 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=639091\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at x=3 and x=0, and a root of multiplicity 1 at x=&#8722;4<BR>\n" );
document.write( "Find a possible formula for P(x).\r<BR>\n" );
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document.write( "with roots at x = 3 and x = 0 and x = -4, your possible factors are:\r<BR>\n" );
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document.write( "(x-3) * x * (x+4)\r<BR>\n" );
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document.write( "the roots at x = 3 and x = 0 have roots of multiplicity 2.\r<BR>\n" );
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document.write( "this means the same root occurs 2 times.\r<BR>\n" );
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document.write( "therefore, your possible factors become:\r<BR>\n" );
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document.write( "(x-3)^2 * x^2 * (x+4)\r<BR>\n" );
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document.write( "if you multiply all these factors together, you get a possible formula for p(x).\r<BR>\n" );
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document.write( "when you multiply the factors together, your equation becomes p(x) = x^5 - 2x^4 - 15x^3 + 36x.\r<BR>\n" );
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document.write( "the graph of that equation is shown below.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/030601.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "if the multiplicity is even, then the graph touches the x-axis but doesn't cross it.\r<BR>\n" );
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document.write( "if the multiplicity is odd, then the graph crosses the x-axis.\r<BR>\n" );
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document.write( "here's a good reference that will help you a lot if you take the time to read it.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/index.htm\" target = \"_blank\">http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/index.htm</a>\r<BR>\n" );
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document.write( "all the tutorials are good, but the ones that refrerence zeroes of polynomials in particular are tutorials 38 and 39.\r<BR>\n" );
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