document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=911773>Question 911773</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The function f is a fifth-degree polynomial help?<BR>\n" );
document.write( "The function f is a fifth-degree polynomial with <BR>\n" );
document.write( "the x-intercepts -1, 4, and 9, <BR>\n" );
document.write( "y-intercept 36 and <BR>\n" );
document.write( "f (x) &#8805; 0 for x &#8804; 9. \r<BR>\n" );
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document.write( "Find f (x). \r<BR>\n" );
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document.write( "f (x) = \r<BR>\n" );
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document.write( "Please explain, <BR>\n" );
document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #553378 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=553378\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We are given; the x-intercepts -1, 4, and 9,<BR>\n" );
document.write( "y-intercept 36 and<BR>\n" );
document.write( "f(x) &#8805; 0 for x &#8804; 9, therefore<BR>\n" );
document.write( "f(x) = (x+1)*(x-4)*(x-9)*g(x) where<BR>\n" );
document.write( "g(x) is a quadratic equation of the form<BR>\n" );
document.write( "Ax^2 + Bx +C<BR>\n" );
document.write( "To determine g(x):<BR>\n" );
document.write( "We need f(x) &#8805; 0 for x &#8804; 9.<BR>\n" );
document.write( "==> (x + 1)(x - 4)(x - 9)g(x) &#8805; 0 for x &#8804; 9.<BR>\n" );
document.write( "Since we need g(x) to be quadratic, we can take g(x) = A(x + 1)(x - 4) for some constant A and<BR>\n" );
document.write( "Now, we have f(x) = A(x + 1)^2*(x - 4)^2*(x - 9) for some A.<BR>\n" );
document.write( "we use f(0) = A(1)^2*(-4)^2*(-9) = 36<BR>\n" );
document.write( "36 = A*(1)*16*(-9)<BR>\n" );
document.write( "36 = -A*144<BR>\n" );
document.write( "A = -1/4<BR>\n" );
document.write( "therefore<BR>\n" );
document.write( "f(x) = (-1/4)*(x + 1)^2*(x - 4)^2*(x - 9)<BR>\n" );
document.write( "f(x) = -x^5/4+(15*x^4)/4-(55*x^3)/4-(15*x^2)/4+50*x+36\r<BR>\n" );
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document.write( "  </SPAN>\n" );
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