document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=152065>Question 152065</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/1565771346/algebrahomeworkh>Algebra 1 An Incremental Development</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Factor: 6x^2 + x - 2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #111787 by </B><A HREF=/tutors/aboutme.mpl?userid=nabla><B>nabla(475)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nabla><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=111787\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 6x^2 + x - 2=(3x+2)(2x-1)\r<BR>\n" );
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document.write( "Explanation:<BR>\n" );
document.write( "Consider:<BR>\n" );
document.write( "ax^2+bx+c\r<BR>\n" );
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document.write( "If we want to factor into form\r<BR>\n" );
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document.write( "(dx+e)(fx+g)\r<BR>\n" );
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document.write( ", we will need df=a, fe+gd=b, and eg=c.\r<BR>\n" );
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document.write( "So, for our problem we have<BR>\n" );
document.write( "a=6, b=1, c=-2\r<BR>\n" );
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document.write( "So we need df=6, fe+gd=1, eg=-2\r<BR>\n" );
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document.write( "Note that d and f must exist in the set A={1,2,3,6}. If we suspect 2 and 3 as d and f, we must must have (1) 2e+3g=1 or (2) 2g+3e=1 with eg still -2.\r<BR>\n" );
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document.write( "However, the same rule applies as with df. eg must have factors existing in B={1,2}. We note that -1(2)=-2 and 1(-2)=-2. Therefore these two are possible values of e and g. However, we must decide which is which.\r<BR>\n" );
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document.write( "For (1) If e=-1 and g=2, -2+6=4 is not equal to 1. If e=1 and g=-2, 2-6=-4 is not equal to 1.\r<BR>\n" );
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document.write( "For (2) If e=-1 and g=2, 4-3=1 is equal to 1. These must be our values.\r<BR>\n" );
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document.write( "Thus we have, e=-1, g=2, d=2, f=3, and the factorization is (2x-1)(3x+2).\r<BR>\n" );
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document.write( "NOTE: This explanation is quite complicated. You will see with some practice that all of the work I displayed here is totally unnecessary. You will be able to factor out of intuition. </SPAN>\n" );
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