document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1081854>Question 1081854</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the polynomial f(x)= x^4 -6x^3 +9x^2 +4x -12 ,\r<BR>\n" );
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document.write( "(I) factorize f(x) completely and hence find the x and y axes intercepts\r<BR>\n" );
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document.write( "(II) state the x coordinates where the graph of y=f(x) cuts the x-axis and where it touches the x-axis\r<BR>\n" );
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document.write( "(III) draw a sign diagram for f(x)\r<BR>\n" );
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document.write( "(IV) discuss the behaviour of f(x) as x = &#8734; and as x = -&#8734;\r<BR>\n" );
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document.write( "(V) sketch the graph of y=f(x), using the information obtained above. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #695899 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39627)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=695899\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Possible roots to try would be  -6,-4,-3,-2,-1,1,2,3,4,6,12 (Rational Roots Theorem).\r<BR>\n" );
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document.write( "2   |    1   -6   9   4    -12\r\n" );
document.write( "    |         2   -8  2     12\r\n" );
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document.write( "        1    -4   1   6     0\r\n" );
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document.write( "3   |    1    -4    1     6\r\n" );
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document.write( "    |          3    -3    -6\r\n" );
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document.write( "         1    -1   -2     0\r\n" );
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document.write( "Partial factorizing gives <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x-2%29%28x-3%29%28x%5E2-x-2%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x-2%29%28x-3%29%28x%5E2-x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The quadratic factor breaks into f being<BR>\n" );
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document.write( "x-intercepts:<BR>\n" );
document.write( "-1, 2, 3\r<BR>\n" );
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document.write( "y-intercept:<BR>\n" );
document.write( "When x=0, y=-12.\r<BR>\n" );
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document.write( "Table of Signs:<BR>\n" );
document.write( "Check inside each interval on x.<BR>\n" );
document.write( "-<BR>\n" );
document.write( "(infin, -1]<BR>\n" );
document.write( "[-1, 2]<BR>\n" );
document.write( "[2, 3]<BR>\n" );
document.write( "[3, infinity)<BR>\n" );
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document.write( "You can determine the result in each interval on your own.\r<BR>\n" );
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