document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=145363>Question 145363</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Factor by grouping <BR>\n" );
document.write( "6c squared 11c - 2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #106049 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=106049\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "Looking at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6c%5E2%2B11c-2 ALIGN=MIDDLE  ALT=\"6c%5E2%2B11c-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can see that the first term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6c%5E2 ALIGN=MIDDLE  ALT=\"6c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the last term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > where the coefficients are 6 and -2 respectively.\r<BR>\n" );
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document.write( "Now multiply the first coefficient 6 and the last coefficient -2 to get -12. Now what two numbers multiply to -12 and add to the  middle coefficient 11? Let's list all of the factors of -12:\r<BR>\n" );
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document.write( "Factors of -12:\r<BR>\n" );
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document.write( "1,2,3,4,6,12\r<BR>\n" );
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document.write( "-1,-2,-3,-4,-6,-12 ...List the negative factors as well. This will allow us to find all possible combinations\r<BR>\n" );
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document.write( "These factors pair up and multiply to -12\r<BR>\n" );
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document.write( "(1)*(-12)\r<BR>\n" );
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document.write( "(2)*(-6)\r<BR>\n" );
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document.write( "(3)*(-4)\r<BR>\n" );
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document.write( "(-1)*(12)\r<BR>\n" );
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document.write( "(-2)*(6)\r<BR>\n" );
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document.write( "(-3)*(4)\r<BR>\n" );
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document.write( "note: remember, the product of a negative and a positive number is a negative number\r<BR>\n" );
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document.write( "Now which of these pairs add to 11? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 11\r<BR>\n" );
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document.write( "<th>First Number</th><th>Second Number</th><th>Sum</th><tr><TD  align=\"center\">1</TD><TD  align=\"center\">-12</TD><TD >1+(-12)=-11</TD></tr><tr><TD  align=\"center\">2</TD><TD  align=\"center\">-6</TD><TD >2+(-6)=-4</TD></tr><tr><TD  align=\"center\">3</TD><TD  align=\"center\">-4</TD><TD >3+(-4)=-1</TD></tr><tr><TD  align=\"center\">-1</TD><TD  align=\"center\">12</TD><TD >-1+12=11</TD></tr><tr><TD  align=\"center\">-2</TD><TD  align=\"center\">6</TD><TD >-2+6=4</TD></tr><tr><TD  align=\"center\">-3</TD><TD  align=\"center\">4</TD><TD >-3+4=1</TD></tr>\n" );
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document.write( "From this list we can see that -1 and 12 add up to 11 and multiply to -12\r<BR>\n" );
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document.write( "Now looking at the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6c%5E2%2B11c-2 ALIGN=MIDDLE  ALT=\"6c%5E2%2B11c-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11c ALIGN=MIDDLE  ALT=\"11c\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1c%2B12c ALIGN=MIDDLE  ALT=\"-1c%2B12c\"   DISABLED_style= \"max-width:90%; height:auto;\" > (notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1c%2B12c ALIGN=MIDDLE  ALT=\"-1c%2B12c\"   DISABLED_style= \"max-width:90%; height:auto;\" > adds up to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11c ALIGN=MIDDLE  ALT=\"11c\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So it is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11c ALIGN=MIDDLE  ALT=\"11c\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6c%5E2%2Bhighlight%28-1c%2B12c%29%2B-2 ALIGN=MIDDLE  ALT=\"6c%5E2%2Bhighlight%28-1c%2B12c%29%2B-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now let's factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6c%5E2-1c%2B12c-2 ALIGN=MIDDLE  ALT=\"6c%5E2-1c%2B12c-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > by grouping:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286c%5E2-1c%29%2B%2812c-2%29 ALIGN=MIDDLE  ALT=\"%286c%5E2-1c%29%2B%2812c-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%286c-1%29%2B2%286c-1%29 ALIGN=MIDDLE  ALT=\"c%286c-1%29%2B2%286c-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" > out of the first group. Factor out the GCF of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > out of the second group\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28c%2B2%29%286c-1%29 ALIGN=MIDDLE  ALT=\"%28c%2B2%29%286c-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Since we have a common term of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6c-1 ALIGN=MIDDLE  ALT=\"6c-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can combine like terms\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6c%5E2-1c%2B12c-2 ALIGN=MIDDLE  ALT=\"6c%5E2-1c%2B12c-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28c%2B2%29%286c-1%29 ALIGN=MIDDLE  ALT=\"%28c%2B2%29%286c-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So this also means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6c%5E2%2B11c-2 ALIGN=MIDDLE  ALT=\"6c%5E2%2B11c-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28c%2B2%29%286c-1%29 ALIGN=MIDDLE  ALT=\"%28c%2B2%29%286c-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6c%5E2%2B11c-2 ALIGN=MIDDLE  ALT=\"6c%5E2%2B11c-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6c%5E2-1c%2B12c-2 ALIGN=MIDDLE  ALT=\"6c%5E2-1c%2B12c-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "     Answer:\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6c%5E2%2B11c-2 ALIGN=MIDDLE  ALT=\"6c%5E2%2B11c-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28c%2B2%29%286c-1%29 ALIGN=MIDDLE  ALT=\"%28c%2B2%29%286c-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
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