document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=994953>Question 994953</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find a polynomial f(x), that has the degree of 4 or less, so<BR>\n" );
document.write( "f(&#8722;2) = 0, f(&#8722;1) = 0, f(0) = 0, f(1) = 9, f(2) = 0. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #613848 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52788)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=613848\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "According to the condition, your polynomial has the roots &nbsp;-2, &nbsp;-1, &nbsp;0, &nbsp;and &nbsp;2.\r<BR>\n" );
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document.write( "Hence, &nbsp;the polynomial is \r<BR>\n" );
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document.write( "f(x) = a*(x-(-2))*(x-(-1))*(x-0)*(x-2) = a*(x+2)*x+1)*x*(x-2), \r<BR>\n" );
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document.write( "where &nbsp;a&nbsp; is a coefficient, &nbsp;an unknown real number.\r<BR>\n" );
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document.write( "To find &nbsp;a, &nbsp;use the condition &nbsp;f(1) = 9. \r<BR>\n" );
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document.write( "Simply substitute &nbsp;x=1&nbsp; into this equation &nbsp;(into the polynomial). &nbsp;You will get \r<BR>\n" );
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document.write( "a*(1+2)*(1+1)*1*(1-2) = 9.\r<BR>\n" );
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document.write( "Simplify the left side. &nbsp;You will get a*3*2*1*(-1) = -6a.\r<BR>\n" );
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document.write( "So, &nbsp;the equation for &nbsp;a&nbsp; is\r<BR>\n" );
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document.write( "-6a = 9.\r<BR>\n" );
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document.write( "Hence, &nbsp;a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9%2F6 ALIGN=MIDDLE  ALT=\"-9%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F2 ALIGN=MIDDLE  ALT=\"-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now your polynomial is \r<BR>\n" );
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document.write( "f(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F2 ALIGN=MIDDLE  ALT=\"-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >*(x+2)*x+1)*x*(x-2).\r<BR>\n" );
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document.write( " </SPAN>\n" );
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