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" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #458619 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39630)</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=458619\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Most of the work is in (a) and (c).  The x-intercepts are the zeros of the function, which you find using Rational Roots Theorem and synthetic division.  The possible zeros to test are plus and minus 4, 2, and 1.  Note that when you find any one of the zeros, you can factor or evaluate the quadratic quotient easily.  You have six possible zeros, but you stand a good chance of needing not more than four synthetic divisions.  \r<BR>\n" );
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document.write( "Testing root of +2:\r<BR>\n" );
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document.write( "+2____|___2___1___-8____-4<BR>\n" );
document.write( "______|<BR>\n" );
document.write( "______|_______4___10____4<BR>\n" );
document.write( "___________________________<BR>\n" );
document.write( "__________2___5___2_____0 _____NO REMAINDER\r<BR>\n" );
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document.write( "So factor into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%28x%5E2%2B5x%2B2%29 ALIGN=MIDDLE  ALT=\"%28x-2%29%28x%5E2%2B5x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The quadratic expression factor is not factorable so use formula for quadratic solution:\r<BR>\n" );
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document.write( "The other two zeros are found to be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-5-sqrt%2817%29%29%2F2 ALIGN=MIDDLE  ALT=\"%28-5-sqrt%2817%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-5%2Bsqrt%2817%29%29%2F2 ALIGN=MIDDLE  ALT=\"%28-5%2Bsqrt%2817%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".... unless I made any mistakes in the way.  As decimal approximations, these two zeros are -4.56 and -0.438.\r<BR>\n" );
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document.write( "Your intervals to check are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C-4.56 ALIGN=MIDDLE  ALT=\"x%3C-4.56\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4.56%3Cx%3C-0.438 ALIGN=MIDDLE  ALT=\"-4.56%3Cx%3C-0.438\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.438%3Cx%3C2 ALIGN=MIDDLE  ALT=\"-0.438%3Cx%3C2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%3Cx ALIGN=MIDDLE  ALT=\"2%3Cx\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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