document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=211128>Question 211128</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How does one factor a polynomial where only two of items have negative exponents?\r<BR>\n" );
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document.write( "3x^-2 -7x^-1 -6 = 0\r<BR>\n" );
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document.write( "1/3x^2 - 1/7x - 6 = 0\r<BR>\n" );
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document.write( "Foil would give (1/3x - 3) (x + 2) - but how to get that - 1/7x in the middle (I can get - 7/3x)? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #159550 by </B><A HREF=/tutors/aboutme.mpl?userid=algebrapro18><B>algebrapro18(249)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=algebrapro18><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=159550\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Simple, you don't factor polynomials with negative exponents.  You put the negative exponents in the denominator and the get a common denominator and solve that way. You will end up having to factor but the exponents will be positive.   <br>\r<BR>\n" );
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document.write( "3x^-2 -7x^-1 -6 = 0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Fx%5E2+-+7%2Fx+-+6+=+0 ALIGN=MIDDLE  ALT=\"3%2Fx%5E2+-+7%2Fx+-+6+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "The common denominator on this problem is going to be x^2 so multiply the second part of the equation by x and the 6 by x^2.  This will get us:<br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283+-+7x+-+6x%5E2%29%2Fx%5E2+=+0 ALIGN=MIDDLE  ALT=\"%283+-+7x+-+6x%5E2%29%2Fx%5E2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "Now we multiply both sides by x^2 and that leaves us with the following polynomial:<br>\r<BR>\n" );
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document.write( "3 - 7x - 6x^2 = 0<br>\r<BR>\n" );
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document.write( "Now we solve this like any regular polynomial.<br>\r<BR>\n" );
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document.write( "3 - 7x - 6x^2 = 0<BR>\n" );
document.write( "6x^2 + 7x - 3 = 0 <BR>\n" );
document.write( "(2x+3)(3x-1) = 0<BR>\n" );
document.write( "2x+3 = 0 and 3x-1 = 0 <BR>\n" );
document.write( "x = -3/2 and x = 1/3<br>\r<BR>\n" );
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document.write( "I will leave the second equation for you to do but its solved in a similar manor.<BR>\n" );
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