document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=701633>Question 701633</A>: <I><SPAN STYLE=\"word-break: break-all;\"> x^3+4x^2+7x=28=0\r<BR>\n" );
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document.write( "find possible rational roots:<BR>\n" );
document.write( "find possible actual roots:\r<BR>\n" );
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document.write( "please </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #432490 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=432490\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Assuming you meant to type: x^3+4x^2+7x+28 = 0 \r<BR>\n" );
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document.write( "Possible Roots: List all the factors of 28\r<BR>\n" );
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document.write( "Possible Roots: 1, 2, 4, 7, 14, 28, -1, -2, -4, -7, -14, -28\r<BR>\n" );
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document.write( "Note: make sure you list the negative factors as well\r<BR>\n" );
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document.write( "Another Note: This trick only works if the leading coefficient is 1 or -1.\r<BR>\n" );
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document.write( "Actual Roots: \r<BR>\n" );
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document.write( "x^3+4x^2+7x+28=0 \r<BR>\n" );
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document.write( "(x^3+4x^2)+(7x+28)=0 \r<BR>\n" );
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document.write( "x^2(x+4)+7(x+4)=0\r<BR>\n" );
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document.write( "(x^2+7)(x+4) = 0\r<BR>\n" );
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document.write( "x^2+7 = 0 or x+4 = 0\r<BR>\n" );
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document.write( "x^2 = -7 or x = -4\r<BR>\n" );
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document.write( "x = sqrt(-7), x = -sqrt(-7), or x = -4\r<BR>\n" );
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document.write( "x = i*sqrt(7), x = -i*sqrt(7), or x = -4\r<BR>\n" );
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document.write( "The actual roots are x = i*sqrt(7), x = -i*sqrt(7), or x = -4\r<BR>\n" );
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document.write( "The first two are complex or imaginary roots. The third root is real and rational.\r<BR>\n" );
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document.write( "The only actual rational root is x = -4\r<BR>\n" );
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