document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1029993>Question 1029993</A>: <I><SPAN STYLE=\"word-break: break-all;\">  f(x)=7x3&#8722;x2+2\r<BR>\n" );
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document.write( "That is the problem. The instructions say ' Use the rational zero theorem to list all possible rational zeros for the given function'. I have tried everything, I just can not figure out this problem! <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 #644904 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=644904\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your equation is:\r<BR>\n" );
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document.write( "y = 7x^3 -x^2 + 2\r<BR>\n" );
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document.write( "the rational roots theorem states:\r<BR>\n" );
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document.write( "if f(x) has integer coefficients and p/q is a rational zero, then p is a factor of the constant term and q is a factor of the leading coefficient.\r<BR>\n" );
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document.write( "the problem states that IF p/q is a rational zero.\r<BR>\n" );
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document.write( "p/q has to be in simplified form, based on the definition.\r<BR>\n" );
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document.write( "to find the possible rational zeroes, you would take all the factors of p and all the factors of q and form all possible fractions of p/q from them.\r<BR>\n" );
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document.write( "in your equation of 7x^3 - x^1 + 2, you get:\r<BR>\n" );
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document.write( "p = 2 and q = 7.\r<BR>\n" );
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document.write( "the factors of 2 are 1 and 2.<BR>\n" );
document.write( "the factors of 7 are 1 and 7.\r<BR>\n" );
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document.write( "the possible factors of p/q are 2/7, 2/1, 1/7, 1/1.\r<BR>\n" );
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document.write( "this results in possible factors or 1, 2, 1/7, 2/7.\r<BR>\n" );
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document.write( "you would then use synthetic division to find out if any of these are solutions to the equation.\r<BR>\n" );
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document.write( "you will find that none of them are.\r<BR>\n" );
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document.write( "if you graph the equation of 7x^3 - x^2 + 2, you will find that it has one zero at -.6142924033.\r<BR>\n" );
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document.write( "this is not a rational number as far as i can tell.\r<BR>\n" );
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document.write( "translate all your possible rational zeroes to decimals and you will find that they are equal to plus or minus 1, 2, .1428571429, .2857142857.\r<BR>\n" );
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document.write( "no cigars.\r<BR>\n" );
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document.write( "i did all the possible combinations and came up with no rational zeroes.\r<BR>\n" );
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document.write( "my worksheet is attached for you to review if you wish.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/041513.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "here's a video on youtube that describe the procedure used by the author in finding the rational roots if they exist.<BR>\n" );
document.write( "he goes one step further and finds all the roots.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.youtube.com/watch?v=hJIgO0T5Wi8\" target = \"_blank\">https://www.youtube.com/watch?v=hJIgO0T5Wi8</a>\r<BR>\n" );
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document.write( "he lists the possible rational roots.<BR>\n" );
document.write( "then he uses synthetic division to narrow down the selections.<BR>\n" );
document.write( "he gets down to the point where he has a quadratic equation left and he then solves for the remaining roots of the quadratic.\r<BR>\n" );
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document.write( "his roots for the equation becomes:\r<BR>\n" );
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document.write( "x = -3 or x = 1 or x = plus or minus sqrt(2).\r<BR>\n" );
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document.write( "the following graph shows the equation he factored using the rational roots theorem and the roots and the factors that are formed from those roots.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/041514.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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