document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=753830>Question 753830</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. Given f(x)=2x^3+x^2-8x-4.  <BR>\n" );
document.write( "(a) Find the x-intercepts of f. <BR>\n" );
document.write( "(b) Find f(0). <BR>\n" );
document.write( "(c) Use test points within the intervals formed by the x-intercepts to determine the sign of f(x) in the interval. <BR>\n" );
document.write( "(d) Graph f(x).  <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #458621 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=458621\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. Given f(x)=2x^3+x^2-8x-4. <BR>\n" );
document.write( "(a) Find the x-intercepts of f.<BR>\n" );
document.write( "use rational roots theorem to solve: <BR>\n" );
document.write( "....0...|.....2......1......-8......-4....<BR>\n" );
document.write( "....1...|.....2......3......-5......-9...<BR>\n" );
document.write( "....2...|.....2......5.......2........0 (2 is a root)<BR>\n" );
document.write( "f(x)=(x-2)(2x^2+5x+2)<BR>\n" );
document.write( "f(x)=(x-1)(2x+1)(x+2)<BR>\n" );
document.write( "roots are: 1, -1/2, -2 (x-intercepts)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "(b) Find f(0).<BR>\n" );
document.write( "f(0)=-4<BR>\n" );
document.write( ".. <BR>\n" );
document.write( "(c) Use test points within the intervals formed by the x-intercepts to determine the sign of f(x) in the interval. <BR>\n" );
document.write( "number line:<BR>\n" );
document.write( "<...-...-2...+....-1/2...-....1....+.....>\r<BR>\n" );
document.write( "\n" );
document.write( "(d) Graph f(x). <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-4%2C+4%2C+-10%2C+10%2C2x%5E3%2Bx%5E2-8x-4%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-4%2C+4%2C+-10%2C+10%2C2x%5E3%2Bx%5E2-8x-4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );