document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=147621>Question 147621</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me, I'm so confused!\r<BR>\n" );
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document.write( "List the possible rational zeros of the function using the rational zero theorem.\r<BR>\n" );
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document.write( "a) f(x)= x^4 - 6x^3 + 8x^2 - 21<BR>\n" );
document.write( "b) h(x)= 5x^4 + 12x^3 - 16x^2 + 10<BR>\n" );
document.write( "c) g(x)= 9x^5 + 3x^3 + 7x - 4\r<BR>\n" );
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document.write( "Find all real zeros of the function.\r<BR>\n" );
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document.write( "g(x)= x^3 + 4x^2 - x - 4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #107996 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=107996\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll do the first two to get you started.\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 -21 (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, \pm3, \pm7, \pm21\">\r<BR>\n" );
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document.write( "Now let's list the factors of 1 (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\">\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{3}{1}, \frac{7}{1}, \frac{21}{1}, \frac{-1}{1}, \frac{-3}{1}, \frac{-7}{1}, \frac{-21}{1}\">\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, 3, 7, 21, -1, -3, -7, -21\">\r<BR>\n" );
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document.write( "<hr>\r<BR>\n" );
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document.write( "b)\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 10 (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, \pm2, \pm5, \pm10\">\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{2}{1}, \frac{2}{5}, \frac{5}{1}, \frac{5}{5}, \frac{10}{1}, \frac{10}{5}, \frac{-1}{1}, \frac{-1}{5}, \frac{-2}{1}, \frac{-2}{5}, \frac{-5}{1}, \frac{-5}{5}, \frac{-10}{1}, \frac{-10}{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}, 2, \frac{2}{5}, 5, 10, -1, \frac{-1}{5}, -2, \frac{-2}{5}, -5, -10\">\r<BR>\n" );
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