document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1183370>Question 1183370</A>: <I><SPAN STYLE=\"word-break: break-all;\"> f(x) = x4 − 12x3 + 37x2 − 12x + 36\r<BR>\n" );
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document.write( "(a) Find all zeros of the function. (Enter your answers as a comma-separated list.)<BR>\n" );
document.write( "x = I found this to be i,-i,6<BR>\n" );
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document.write( "(b) Write the polynomial as a product of linear factors.<BR>\n" );
document.write( "f(x) = <BR>\n" );
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document.write( "(c) Use your factorization to determine the x-intercepts of the graph of the function. Use a graphing utility to verify that the real zeros are the only x-intercepts. (Enter your answers as a comma-separated list. If no x-intercepts exist, enter DNE.)<BR>\n" );
document.write( "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 #813662 by </B><A HREF=/tutors/aboutme.mpl?userid=Solver92311><B>Solver92311(821)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Solver92311><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=Solver92311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=813662\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Your answer to part a is incorrect.  Since you started with a 4th-degree polynomial, the fundamental theorem of algebra demands that you have 4 zeros counting multiplicities.  You only list 3.  Hint: One of your listed zeros has a multiplicity of 2.\r<BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a\"> is a zero of a polynomial, then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ -\ a\"> is a factor of the polynomial.  Since you have four zeros, you need to have four factors.\r<BR>\n" );
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document.write( "Any real number zeros are <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">-intercepts.  Hint: when you have an even-numbered multiplicity, the graph is tangent to the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">-axis.\r<BR>\n" );
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document.write( "																<BR>\n" );
document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "From <https://www.algebra.com/cgi-bin/upload-illustration.mpl> <BR>\n" );
document.write( "I > Ø<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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