document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=467453>Question 467453</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find a third–degree polynomial function such that f(0) = 18 and whose zeros are –1, 2, and 3. Using complete sentences, explain how you found it.<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 #320763 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=320763\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> -1 a root means x + 1 is a factor of the polynomial<BR>\n" );
document.write( "2 a root means x - 2 is a factor of the polynomial<BR>\n" );
document.write( "3 a root means x - 3 is a factor of the polynomial\r<BR>\n" );
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document.write( "==> The polynomial is of the form f(x) = a(x+1)(x-2)(x-3), where a is an undetermined coefficient.  To find the value of c, use the boundary condition f(0) = 18.\r<BR>\n" );
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document.write( "==> f(0) = c(0+1)(0-2)(0-3) = c*1*-2*-3 = 6c = 18 ==> c = 3.\r<BR>\n" );
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document.write( "Hence the polynomial is f(x) = 3(x+1)(x-2)(x-3).  I leave it up to you to multiply out the linear factors. </SPAN>\n" );
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