document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=947522>Question 947522</A>: <I><SPAN STYLE=\"word-break: break-all;\"> P(x) = 3x^3 + x2 &#8722; 7x &#8722; 5 What are all possible rational zeros of P given by the Rational Zeros Theorem? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #578211 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=578211\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the rational roots are all the possible factors of p divided by q after you have reduced that fraction to simplest terms.\r<BR>\n" );
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document.write( "p is the constant term.<BR>\n" );
document.write( "q is the leading coefficient.\r<BR>\n" );
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document.write( "your p is equal to 5<BR>\n" );
document.write( "your q is equal to 3\r<BR>\n" );
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document.write( "the possible factors of 5 are 1,5<BR>\n" );
document.write( "the possible factors of q are 1,3\r<BR>\n" );
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document.write( "the possible factors of p/q are 1/1, 1/3, 5/1, 5/3.\r<BR>\n" );
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document.write( "the possible rational roots are plus or minus the possible factors of p/q.\r<BR>\n" );
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document.write( "as it turns out, the roots are x = -1 and x = 5/3.\r<BR>\n" );
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document.write( "a graph of the equation is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/021401.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "1.667 shown on the graph is equal to 1 and 2/3 which is equal to 5/3.\r<BR>\n" );
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document.write( "the solution of x = -1 is actually encountered twice, so the factors of the equation are:\r<BR>\n" );
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document.write( "(x+1) * (x+1) * (x-5/3) = 0\r<BR>\n" );
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document.write( "if you multiply those factors out, you will get back to the original equation.\r<BR>\n" );
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document.write( "so you have 3 rational roots to the equation.\r<BR>\n" );
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document.write( "-1 is encountered twice and 5/3 is encountered once.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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