document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=649634>Question 649634</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Need help factoring this, not solving.<BR>\n" );
document.write( "2a^2-11a+7 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #407028 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><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=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=407028\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In order to factor this expression, you must use the quadratic formula. From the solution, you can factor this since there are no rational solutions to this equation (if set to 0).\r<BR>\n" );
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document.write( "Before we go through this, it's easy to see that if we did have rational solutions, we'd have a (2a?7) and a (a?1) as our factors where ? is either + or -. We can further deduce that both must be - since the middle term is negative.\r<BR>\n" );
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document.write( "This means that we have (2a-7)(a-1); however, if we check this, we get 2a^2 -7a -2a +7 = 2a^2 -9a +7\r<BR>\n" );
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document.write( "So let's use the quadratic formula: for ax^2+bx+c\r<BR>\n" );
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document.write( "a = 2  b = -11 c = 7\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2811+%2B-+sqrt%28121+-56%29%29%2F4+=+%2811%2B-sqrt%2865%29%29%2F4 ALIGN=MIDDLE  ALT=\"%2811+%2B-+sqrt%28121+-56%29%29%2F4+=+%2811%2B-sqrt%2865%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This means that x-(11+sqrt(65))/4 = 0 and x-(11-sqrt(65))/4 = 0\r<BR>\n" );
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document.write( "Multiply both sides by 4 to get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+-11+%2B+sqrt%2865%29 ALIGN=MIDDLE  ALT=\"4x+-11+%2B+sqrt%2865%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0   and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+-+11+-sqrt%2865%29+=+0 ALIGN=MIDDLE  ALT=\"4x+-+11+-sqrt%2865%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So to factor this we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F8%29%284a%2Bsqrt%2865%29-+11%29%284a-sqrt%2865%29-11%29 ALIGN=MIDDLE  ALT=\"%281%2F8%29%284a%2Bsqrt%2865%29-+11%29%284a-sqrt%2865%29-11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---answer\r<BR>\n" );
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document.write( "FOIL this out to get (1/8)(16a^2 -88a +56) = 2a^2-11a+7. Good.\r<BR>\n" );
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