document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209234>Question 1209234</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Fill in the blank with a constant, so that the resulting expression can be<BR>\n" );
document.write( "factored as the product of two linear expressions:\r<BR>\n" );
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document.write( "2ab - a + b + ___ </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #847892 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=847892\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2ab-a%2Bb%2Bx ALIGN=MIDDLE  ALT=\"2ab-a%2Bb%2Bx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Group the first two terms and take out the common factor.  (You could equally well group the first and third terms and proceed in a similar manner.)<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%282b-1%29%2B%28b%2Bx%29 ALIGN=MIDDLE  ALT=\"a%282b-1%29%2B%28b%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "We need to write the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b%2Bx%29 ALIGN=MIDDLE  ALT=\"%28b%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the form where it is a constant times the factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282b-1%29 ALIGN=MIDDLE  ALT=\"%282b-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2Bx=n%282b-1%29 ALIGN=MIDDLE  ALT=\"b%2Bx=n%282b-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Clearly the constant n must be 1/2.  That gives us<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%282b-1%29%2B%281%2F2%29%282b-1%29=2ab-a%2Bb-1%2F2 ALIGN=MIDDLE  ALT=\"a%282b-1%29%2B%281%2F2%29%282b-1%29=2ab-a%2Bb-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: -1/2<br><BR>\n" );
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