document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=762287>Question 762287</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the lowest degree polynomial f(x) that match the graph below. Leave your answer in factored form.\r<BR>\n" );
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document.write( "Graph: <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 #463835 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=463835\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are 3 roots, and the roots on the very left and very right are double roots (since they only touch the x axis and does not pass through)\r<BR>\n" );
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document.write( "So there are really 2+1+2 = 5 roots total (2 of which are repeating, only one is a non-repeating root)\r<BR>\n" );
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document.write( "So the lowest possible degree is a 5th degree polynomial.\r<BR>\n" );
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document.write( "The roots are: -6, 2, 5\r<BR>\n" );
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document.write( "The factors would then be:  x - (-6), x-2, x-5 which turn into:  x-6, x-2, x-5\r<BR>\n" );
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document.write( "But remember -6 and 5 are double roots, so the factors are really (x-6)^2, (x-2), (x-5)^2\r<BR>\n" );
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document.write( "Put this all together to get (x-6)^2 * (x-2) * (x-5)^2\r<BR>\n" );
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document.write( "Then stick a constant k out front to get:  k*(x-6)^2 * (x-2) * (x-5)^2\r<BR>\n" );
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document.write( "Because f(0) = 4, we know that  \r<BR>\n" );
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document.write( "f(x) = k*(x-6)^2 * (x-2) * (x-5)^2\r<BR>\n" );
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document.write( "f(0) = k*(0-6)^2 * (0-2) * (0-5)^2\r<BR>\n" );
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document.write( "4 = k*(0-6)^2 * (0-2) * (0-5)^2\r<BR>\n" );
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document.write( "Now solve for k </SPAN>\n" );
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