document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=916872>Question 916872</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How to find the leading coefficient with graph provided?\r<BR>\n" );
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document.write( "http://i.imgur.com/hslfSWo.png\r<BR>\n" );
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document.write( "I know that it has 4 degrees and it looks like: P(x)=(x+3)(x+1)^2(x-2) but I just cant seem to figure out what the leading coefficient is I know it's negative since the graphing is downwards, does it have something to do with the y-intercept?\r<BR>\n" );
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document.write( "Please help!<BR>\n" );
document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #556359 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=556359\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=%28x%2B3%29%28x%2B1%29%5E2%28x-2%29 ALIGN=MIDDLE  ALT=\"P%28x%29=%28x%2B3%29%28x%2B1%29%5E2%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...  here you did use given roots correctly\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=+highlight%281%29x%5E4%2B3x%5E3-3x%5E2-11x-6 ALIGN=MIDDLE  ALT=\"P%28x%29+=+highlight%281%29x%5E4%2B3x%5E3-3x%5E2-11x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > ..this is expended form where the leading coefficient is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%281%29 ALIGN=MIDDLE  ALT=\"highlight%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "but, you are also given y-intercept (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" >)  we need <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "instead <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6 ALIGN=MIDDLE  ALT=\"-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=+highlight%281%29x%5E4%2B3x%5E3-3x%5E2-11x-6 ALIGN=MIDDLE  ALT=\"P%28x%29+=+highlight%281%29x%5E4%2B3x%5E3-3x%5E2-11x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so,  we need to multiply each term by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=+highlight%28-2%29x%5E4-6x%5E3%2B6x%5E2%2B22x%2B12 ALIGN=MIDDLE  ALT=\"P%28x%29+=+highlight%28-2%29x%5E4-6x%5E3%2B6x%5E2%2B22x%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" >; the leading coefficient you are looking for is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28-2%29 ALIGN=MIDDLE  ALT=\"highlight%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and as a product:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=+-2%28x-2%29%28x%2B1%29%5E2%28x%2B3%29+ ALIGN=MIDDLE  ALT=\"P%28x%29+=+-2%28x-2%29%28x%2B1%29%5E2%28x%2B3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+25%2Ccircle%280%2C12%2C.2%29%2C++circle%282%2C0%2C.2%29%2C++circle%28-1%2C0%2C.2%29%2C++circle%28-3%2C0%2C.2%29%2C++graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+25%2C+-2%28x-2%29%28x%2B1%29%5E2%28x%2B3%29%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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