document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=193568>Question 193568</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with the following problem. <BR>\n" );
document.write( "Suppose f(x)=5x^3-4x^2-5x-35\r<BR>\n" );
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document.write( "a) list all possible rational zeros for the polynomial<BR>\n" );
document.write( "b) Use synthetic division to find at least 1 rational zero.\r<BR>\n" );
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document.write( "For the possible rational zeros I found: +/- 1, +/- 1/5, +/- 5, +/- 7, +/- 7/5,     +/- 35. Is there one that I am missing? Because when I graphed it on the calculator there was a zero at 12/5 or 2.4 and none of my zeros equal that.\r<BR>\n" );
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document.write( "Please help me at your earliest convenience\r<BR>\n" );
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document.write( "thanks<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 #145287 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=145287\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You have to be careful when it comes to using the graphing calculator to find the solutions. It turns out that 2.414679875... is a solution (not 2.4). So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F5 ALIGN=MIDDLE  ALT=\"12%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > is NOT a solution.\r<BR>\n" );
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document.write( "a)\r<BR>\n" );
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document.write( "Any rational zero can be found through this equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE Roots=\frac{p}{q}\"> where p and q are the factors of the last and first coefficients\r<BR>\n" );
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document.write( "So let's list the factors of 35 (the last coefficient):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE p=\pm1, \pm5, \pm7, \pm35\">\r<BR>\n" );
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document.write( "Now let's list the factors of 5 (the first coefficient):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE q=\pm1, \pm5\">\r<BR>\n" );
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document.write( "Now let's divide each factor of the last coefficient by each factor of the first coefficient\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{1}{1}, \frac{1}{5}, \frac{5}{1}, \frac{5}{5}, \frac{7}{1}, \frac{7}{5}, \frac{35}{1}, \frac{35}{5}, \frac{-1}{1}, \frac{-1}{5}, \frac{-5}{1}, \frac{-5}{5}, \frac{-7}{1}, \frac{-7}{5}, \frac{-35}{1}, \frac{-35}{5}\">\r<BR>\n" );
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document.write( "Now simplify\r<BR>\n" );
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document.write( "These are all the distinct rational zeros of the function that could occur\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE  1, \frac{1}{5}, 5, 7, \frac{7}{5}, 35, -1, -\frac{1}{5}, -5, -7, -\frac{7}{5}, -35\">\r<BR>\n" );
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document.write( "which can be sorted and rewritten as\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE  \pm \frac{1}{5}, \pm 1, \pm \frac{7}{5}, \pm 5, \pm 7, \pm 35\">\r<BR>\n" );
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document.write( "So you have the correct possible rational roots.\r<BR>\n" );
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document.write( "b)\r<BR>\n" );
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document.write( "From here, simply perform synthetic division using all of the possible zeros to determine which possible roots are actual roots.\r<BR>\n" );
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