document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1053459>Question 1053459</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What are the zeros and the multiplicity of the following function? <BR>\n" );
document.write( "F(x)=x^4-x^3-2x^2  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #668692 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=668692\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> F(x)=x^4-x^3-2x^2 <BR>\n" );
document.write( "factor out an x^2(x^2-x-2)<BR>\n" );
document.write( "then factor x^2-x-2 into (x-2)(x+1)<BR>\n" );
document.write( "x^2(x-2)(x+1). x^2 has multiplicity 2, and the graph shows a \"bounce\" at the origin.<BR>\n" );
document.write( "zeros are at -1,0(multiplicity 2), and 2.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E4-x%5E3-2x%5E2%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E4-x%5E3-2x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );