document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=171535>Question 171535</A>: <I><SPAN STYLE=\"word-break: break-all;\">   \r<BR>\n" );
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document.write( "Factor each expression completely.<BR>\n" );
document.write( "1.   12x2 + 6x + 18  <BR>\n" );
document.write( "3(2x2 + x + 3)<BR>\n" );
document.write( "6(2x2 + x + 3)<BR>\n" );
document.write( "3(2x – 1)(x + 3)<BR>\n" );
document.write( "6(2x – 1)(x + 3)\r<BR>\n" );
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document.write( "2.   m2 + 11m + 18  <BR>\n" );
document.write( "(m – 2)(m + 9)<BR>\n" );
document.write( "(m + 2)(m + 9)<BR>\n" );
document.write( "(m – 3)(m + 6)<BR>\n" );
document.write( "(m + 3)(m + 6)\r<BR>\n" );
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document.write( "3.   x2 – 14x – 15  <BR>\n" );
document.write( "(x – 5)(x + 3)<BR>\n" );
document.write( "(x + 5)(x – 3)<BR>\n" );
document.write( "(x – 15)(x + 1)<BR>\n" );
document.write( "(x + 15)(x – 1)\r<BR>\n" );
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document.write( "4.   x2 – 13x + 42 <BR>\n" );
document.write( "(x + 6)(x – 7)<BR>\n" );
document.write( "(x – 6)(x + 7)<BR>\n" );
document.write( "(x – 6)(x – 7)<BR>\n" );
document.write( "(x + 6)(x + 7)\r<BR>\n" );
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document.write( "5.   64x2 + 144x + 81  <BR>\n" );
document.write( "(8x – 9)2<BR>\n" );
document.write( "(8x + 9)2<BR>\n" );
document.write( "2(8x + 9)<BR>\n" );
document.write( "(8x + 9)(8x – 9)\r<BR>\n" );
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document.write( "6.   3x2 + 5x – 50  <BR>\n" );
document.write( "(x – 25)(3x + 2)<BR>\n" );
document.write( "(3x – 25)(x + 2)<BR>\n" );
document.write( "(x – 10)(3x + 5)<BR>\n" );
document.write( "(3x – 10)(x + 5)\r<BR>\n" );
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document.write( "7.   5k2 – 125  <BR>\n" );
document.write( "(k – 5)2<BR>\n" );
document.write( "5(k – 5)2<BR>\n" );
document.write( "(k + 5)(k – 5)<BR>\n" );
document.write( "5(k + 5)(k – 5)\r<BR>\n" );
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document.write( "8.   15n2 – 8n +1  <BR>\n" );
document.write( "(5n + 1)(3n + 1)<BR>\n" );
document.write( "(5n – 1)(3n – 1)<BR>\n" );
document.write( "(5n + 1)(3n – 1)<BR>\n" );
document.write( "(5n – 1)(3n + 1)<BR>\n" );
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document.write( "   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #126698 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=126698\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll do the first three to get you started\r<BR>\n" );
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document.write( "# 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x%5E2%2B6x%2B18 ALIGN=MIDDLE  ALT=\"12x%5E2%2B6x%2B18\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%282x%5E2%2Bx%2B3%29 ALIGN=MIDDLE  ALT=\"6%282x%5E2%2Bx%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now let's focus on the inner expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2Bx%2B3 ALIGN=MIDDLE  ALT=\"2x%5E2%2Bx%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Looking at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B1x%2B3 ALIGN=MIDDLE  ALT=\"2x%5E2%2B1x%2B3\"   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=2x%5E2 ALIGN=MIDDLE  ALT=\"2x%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=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > where the coefficients are 2 and 3 respectively.\r<BR>\n" );
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document.write( "Now multiply the first coefficient 2 and the last coefficient 3 to get 6. Now what two numbers multiply to 6 and add to the  middle coefficient 1? Let's list all of the factors of 6:\r<BR>\n" );
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document.write( "Factors of 6:\r<BR>\n" );
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document.write( "1,2,3,6\r<BR>\n" );
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document.write( "-1,-2,-3,-6 ...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 6\r<BR>\n" );
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document.write( "1*6\r<BR>\n" );
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document.write( "2*3\r<BR>\n" );
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document.write( "(-1)*(-6)\r<BR>\n" );
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document.write( "(-2)*(-3)\r<BR>\n" );
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document.write( "note: remember two negative numbers multiplied together make a positive number\r<BR>\n" );
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document.write( "Now which of these pairs add to 1? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 1\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\">6</TD><TD >1+6=7</TD></tr><tr><TD  align=\"center\">2</TD><TD  align=\"center\">3</TD><TD >2+3=5</TD></tr><tr><TD  align=\"center\">-1</TD><TD  align=\"center\">-6</TD><TD >-1+(-6)=-7</TD></tr><tr><TD  align=\"center\">-2</TD><TD  align=\"center\">-3</TD><TD >-2+(-3)=-5</TD></tr>\n" );
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document.write( "None of these pairs of factors add to 1. So the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2Bx%2B3 ALIGN=MIDDLE  ALT=\"2x%5E2%2Bx%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > cannot be factored\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%282x%5E2%2Bx%2B3%29 ALIGN=MIDDLE  ALT=\"6%282x%5E2%2Bx%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > just remains as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%282x%5E2%2Bx%2B3%29 ALIGN=MIDDLE  ALT=\"6%282x%5E2%2Bx%2B3%29\"   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=12x%5E2%2B6x%2B18 ALIGN=MIDDLE  ALT=\"12x%5E2%2B6x%2B18\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%282x%5E2%2Bx%2B3%29 ALIGN=MIDDLE  ALT=\"6%282x%5E2%2Bx%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "    \r<BR>\n" );
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document.write( "# 2\r<BR>\n" );
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document.write( "Looking at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1m%5E2%2B11m%2B18 ALIGN=MIDDLE  ALT=\"1m%5E2%2B11m%2B18\"   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=1m%5E2 ALIGN=MIDDLE  ALT=\"1m%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=18 ALIGN=MIDDLE  ALT=\"18\"   DISABLED_style= \"max-width:90%; height:auto;\" > where the coefficients are 1 and 18 respectively.\r<BR>\n" );
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document.write( "Now multiply the first coefficient 1 and the last coefficient 18 to get 18. Now what two numbers multiply to 18 and add to the  middle coefficient 11? Let's list all of the factors of 18:\r<BR>\n" );
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document.write( "Factors of 18:\r<BR>\n" );
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document.write( "1,2,3,6,9,18\r<BR>\n" );
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document.write( "-1,-2,-3,-6,-9,-18 ...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 18\r<BR>\n" );
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document.write( "1*18\r<BR>\n" );
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document.write( "2*9\r<BR>\n" );
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document.write( "3*6\r<BR>\n" );
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document.write( "(-1)*(-18)\r<BR>\n" );
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document.write( "(-2)*(-9)\r<BR>\n" );
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document.write( "(-3)*(-6)\r<BR>\n" );
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document.write( "note: remember two negative numbers multiplied together make a positive 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\">18</TD><TD >1+18=19</TD></tr><tr><TD  align=\"center\">2</TD><TD  align=\"center\">9</TD><TD >2+9=11</TD></tr><tr><TD  align=\"center\">3</TD><TD  align=\"center\">6</TD><TD >3+6=9</TD></tr><tr><TD  align=\"center\">-1</TD><TD  align=\"center\">-18</TD><TD >-1+(-18)=-19</TD></tr><tr><TD  align=\"center\">-2</TD><TD  align=\"center\">-9</TD><TD >-2+(-9)=-11</TD></tr><tr><TD  align=\"center\">-3</TD><TD  align=\"center\">-6</TD><TD >-3+(-6)=-9</TD></tr>\n" );
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document.write( "From this list we can see that 2 and 9 add up to 11 and multiply to 18\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=1m%5E2%2B11m%2B18 ALIGN=MIDDLE  ALT=\"1m%5E2%2B11m%2B18\"   DISABLED_style= \"max-width:90%; height:auto;\" >, replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11m ALIGN=MIDDLE  ALT=\"11m\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2m%2B9m ALIGN=MIDDLE  ALT=\"2m%2B9m\"   DISABLED_style= \"max-width:90%; height:auto;\" > (notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2m%2B9m ALIGN=MIDDLE  ALT=\"2m%2B9m\"   DISABLED_style= \"max-width:90%; height:auto;\" > adds up to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11m ALIGN=MIDDLE  ALT=\"11m\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So it is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11m ALIGN=MIDDLE  ALT=\"11m\"   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=1m%5E2%2B2m%2B9m%2B18 ALIGN=MIDDLE  ALT=\"1m%5E2%2B2m%2B9m%2B18\"   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=%281m%5E2%2B2m%29%2B%289m%2B18%29 ALIGN=MIDDLE  ALT=\"%281m%5E2%2B2m%29%2B%289m%2B18%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=m%28m%2B2%29%2B9%28m%2B2%29 ALIGN=MIDDLE  ALT=\"m%28m%2B2%29%2B9%28m%2B2%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=m ALIGN=MIDDLE  ALT=\"m\"   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=9 ALIGN=MIDDLE  ALT=\"9\"   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=%28m%2B9%29%28m%2B2%29 ALIGN=MIDDLE  ALT=\"%28m%2B9%29%28m%2B2%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=m%2B2 ALIGN=MIDDLE  ALT=\"m%2B2\"   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=1m%5E2%2B2m%2B9m%2B18 ALIGN=MIDDLE  ALT=\"1m%5E2%2B2m%2B9m%2B18\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28m%2B9%29%28m%2B2%29 ALIGN=MIDDLE  ALT=\"%28m%2B9%29%28m%2B2%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=1m%5E2%2B11m%2B18 ALIGN=MIDDLE  ALT=\"1m%5E2%2B11m%2B18\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28m%2B9%29%28m%2B2%29 ALIGN=MIDDLE  ALT=\"%28m%2B9%29%28m%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1m%5E2%2B11m%2B18 ALIGN=MIDDLE  ALT=\"1m%5E2%2B11m%2B18\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1m%5E2%2B2m%2B9m%2B18 ALIGN=MIDDLE  ALT=\"1m%5E2%2B2m%2B9m%2B18\"   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=m%5E2%2B11m%2B18 ALIGN=MIDDLE  ALT=\"m%5E2%2B11m%2B18\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28m%2B9%29%28m%2B2%29 ALIGN=MIDDLE  ALT=\"%28m%2B9%29%28m%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "# 3\r<BR>\n" );
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document.write( "Looking at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2-14x-15 ALIGN=MIDDLE  ALT=\"1x%5E2-14x-15\"   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=1x%5E2 ALIGN=MIDDLE  ALT=\"1x%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=-15 ALIGN=MIDDLE  ALT=\"-15\"   DISABLED_style= \"max-width:90%; height:auto;\" > where the coefficients are 1 and -15 respectively.\r<BR>\n" );
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document.write( "Now multiply the first coefficient 1 and the last coefficient -15 to get -15. Now what two numbers multiply to -15 and add to the  middle coefficient -14? Let's list all of the factors of -15:\r<BR>\n" );
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document.write( "Factors of -15:\r<BR>\n" );
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document.write( "1,3,5,15\r<BR>\n" );
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document.write( "-1,-3,-5,-15 ...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 -15\r<BR>\n" );
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document.write( "(1)*(-15)\r<BR>\n" );
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document.write( "(3)*(-5)\r<BR>\n" );
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document.write( "(-1)*(15)\r<BR>\n" );
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document.write( "(-3)*(5)\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 -14? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -14\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\">-15</TD><TD >1+(-15)=-14</TD></tr><tr><TD  align=\"center\">3</TD><TD  align=\"center\">-5</TD><TD >3+(-5)=-2</TD></tr><tr><TD  align=\"center\">-1</TD><TD  align=\"center\">15</TD><TD >-1+15=14</TD></tr><tr><TD  align=\"center\">-3</TD><TD  align=\"center\">5</TD><TD >-3+5=2</TD></tr>\n" );
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document.write( "From this list we can see that 1 and -15 add up to -14 and multiply to -15\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=1x%5E2-14x-15 ALIGN=MIDDLE  ALT=\"1x%5E2-14x-15\"   DISABLED_style= \"max-width:90%; height:auto;\" >, replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-14x ALIGN=MIDDLE  ALT=\"-14x\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%2B-15x ALIGN=MIDDLE  ALT=\"1x%2B-15x\"   DISABLED_style= \"max-width:90%; height:auto;\" > (notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%2B-15x ALIGN=MIDDLE  ALT=\"1x%2B-15x\"   DISABLED_style= \"max-width:90%; height:auto;\" > adds up to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-14x ALIGN=MIDDLE  ALT=\"-14x\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So it is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-14x ALIGN=MIDDLE  ALT=\"-14x\"   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=1x%5E2%2Bhighlight%281x%2B-15x%29%2B-15 ALIGN=MIDDLE  ALT=\"1x%5E2%2Bhighlight%281x%2B-15x%29%2B-15\"   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=1x%5E2%2B1x-15x-15 ALIGN=MIDDLE  ALT=\"1x%5E2%2B1x-15x-15\"   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=%281x%5E2%2B1x%29%2B%28-15x-15%29 ALIGN=MIDDLE  ALT=\"%281x%5E2%2B1x%29%2B%28-15x-15%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=x%28x%2B1%29-15%28x%2B1%29 ALIGN=MIDDLE  ALT=\"x%28x%2B1%29-15%28x%2B1%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=x ALIGN=MIDDLE  ALT=\"x\"   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=-15 ALIGN=MIDDLE  ALT=\"-15\"   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=%28x-15%29%28x%2B1%29 ALIGN=MIDDLE  ALT=\"%28x-15%29%28x%2B1%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=x%2B1 ALIGN=MIDDLE  ALT=\"x%2B1\"   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=1x%5E2%2B1x-15x-15 ALIGN=MIDDLE  ALT=\"1x%5E2%2B1x-15x-15\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-15%29%28x%2B1%29 ALIGN=MIDDLE  ALT=\"%28x-15%29%28x%2B1%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=1x%5E2-14x-15 ALIGN=MIDDLE  ALT=\"1x%5E2-14x-15\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-15%29%28x%2B1%29 ALIGN=MIDDLE  ALT=\"%28x-15%29%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2-14x-15 ALIGN=MIDDLE  ALT=\"1x%5E2-14x-15\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B1x-15x-15 ALIGN=MIDDLE  ALT=\"1x%5E2%2B1x-15x-15\"   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=x%5E2-14x-15 ALIGN=MIDDLE  ALT=\"x%5E2-14x-15\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-15%29%28x%2B1%29 ALIGN=MIDDLE  ALT=\"%28x-15%29%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );