document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=994806>Question 994806</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me and show step by step.\r<BR>\n" );
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document.write( "1.The polynomial of degree 4, P(x)  has a root of multiplicity 2 at x=4  and roots of multiplicity 1 at x=0  and x=&#8722;3 . It goes through the point (5,32) . <BR>\n" );
document.write( " Find a 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 #613782 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=613782\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Root x=4 of multiplicity 2 means that P(x) has a factor (x-4)^2<BR>\n" );
document.write( "Roots of multiplicity 1 at x=0 means P(x) has a factor x and at<BR>\n" );
document.write( "x=-3 means a factor (x+3) <BR>\n" );
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document.write( "P(x) = x * (x-4)^2 * (x+3)<BR>\n" );
document.write( "P(x) = (x^2+3x) * (x-4)^2<BR>\n" );
document.write( "P(x) = (x^2+3x) * (x^2 -8x +16)<BR>\n" );
document.write( "P(x) = x^4 -5x^3 -8x^2 +48x<BR>\n" );
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document.write( "now we use point (5,32)<BR>\n" );
document.write( "32 = 5^4 -5(5^3) -8(5^2) +48(5)<BR>\n" );
document.write( "32 = 625 -625 -200 +240<BR>\n" );
document.write( "to make this work we have to subtract 8 from the right side of =, therefore<BR>\n" );
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document.write( "P(x) = x^4 -5x^3 -8x^2 +48x -8 and then<BR>\n" );
document.write( "32 = 32<BR>\n" );
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