document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1098319>Question 1098319</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the zeros, the degree, and the leading coefficient to graph this function.  \r<BR>\n" );
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document.write( "f(x) = (x2+2x)(x-3) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #712675 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=712675\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Usually, we write exponents following a ^ symbol.<BR>\n" );
document.write( "Write <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > as x^2 , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3 ALIGN=MIDDLE  ALT=\"x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > as x^3 and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as sqrt(2),<BR>\n" );
document.write( "and people will know what you mean.<BR>\n" );
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document.write( "You probably mean<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x%5E2%2B2x%29%28x-3%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%5E2%2B2x%29%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Factorinng further the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2x=x%28x%2B2%29 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x=x%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > factor,<BR>\n" );
document.write( "you can re-write the fucntion as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%28x%2B2%29%28x-3%29 ALIGN=MIDDLE  ALT=\"f%28x%29=x%28x%2B2%29%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "When one of those three factors is zero, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=0 ALIGN=MIDDLE  ALT=\"f%28x%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so the zeros of the function are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=0%29 ALIGN=MIDDLE  ALT=\"highlight%28x=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2=0 ALIGN=MIDDLE  ALT=\"x%2B2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=-2%29 ALIGN=MIDDLE  ALT=\"highlight%28x=-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3=0 ALIGN=MIDDLE  ALT=\"x-3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=3%29 ALIGN=MIDDLE  ALT=\"highlight%28x=3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
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document.write( "Doing the indicated multiplication,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x%5E2%2B2x%29%28x-3%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%5E2%2B2x%29%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be re-written as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E3-3x%5E2%2B2x%5E2-6x ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E3-3x%5E2%2B2x%5E2-6x\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and \"collecting like terms, we simplify it to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E3-x%5E2-6x ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E3-x%5E2-6x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The leading coefficient is the number part of the term of highest degree.<BR>\n" );
document.write( "That is the implied/invisible <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;\" > in front of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3 ALIGN=MIDDLE  ALT=\"x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The degree is the greatest exponent: the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%283%29 ALIGN=MIDDLE  ALT=\"highlight%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3 ALIGN=MIDDLE  ALT=\"x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
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