document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=916833>Question 916833</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Figuring out graphing of this polynomial:\r<BR>\n" );
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document.write( "f(x) = 12x^3 - 12x^2 - 24x\r<BR>\n" );
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document.write( "what I have so far:<BR>\n" );
document.write( "I know I can factor it down, therefore 12x(x+1)(x-2)<BR>\n" );
document.write( "and the x-int would be (-1,0),(2,0)<BR>\n" );
document.write( "But why is (0,0) also a factor? I don't understand that.\r<BR>\n" );
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document.write( "also how would I find the degree and leading coefficient? very lost on that concept\r<BR>\n" );
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document.write( "And when I plug this poly into a graphing calculator it has a steepness and a lowness at two points. I am in precalculus so I don't know the finer details of graphing/derivatives and I must be able to do this freehand how would I know how far up to make the graph and how far low to make the graph?\r<BR>\n" );
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document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #556318 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</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=556318\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> But WHY is (0,0) also a factor?\r<BR>\n" );
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document.write( "I just answered this question a few minutes ago.\r<BR>\n" );
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document.write( "LOOK at the factorization of f(x).  You have the correct factorization.  Three separate factors written in x.<BR>\n" );
document.write( "The list of factors:<BR>\n" );
document.write( "x<BR>\n" );
document.write( "(x+1)<BR>\n" );
document.write( "(x-2)\r<BR>\n" );
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document.write( "Each of those gives a x-intercept.<BR>\n" );
document.write( "Note that one of the factors is x, so this means that when x=0, f is also zero, BECAUSE x IS ONE OF THE FACTORS OF THE FUNCTION f. </SPAN>\n" );
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