document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=337791>Question 337791</A>: <I><SPAN STYLE=\"word-break: break-all;\"> factor\r<BR>\n" );
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document.write( "3s^2-14s+8\r<BR>\n" );
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document.write( "9v^2+11v+4\r<BR>\n" );
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document.write( "4r^2-22r+10\r<BR>\n" );
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document.write( "b^2-1/2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #242200 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=242200\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Please only post one problem at a time.\r<BR>\n" );
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document.write( "Looking at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3s%5E2-14s%2B8 ALIGN=MIDDLE  ALT=\"3s%5E2-14s%2B8\"   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=3s%5E2 ALIGN=MIDDLE  ALT=\"3s%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=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" > where the coefficients are 3 and 8 respectively.\r<BR>\n" );
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document.write( "Now multiply the first coefficient 3 and the last coefficient 8 to get 24. Now what two numbers multiply to 24 and add to the  middle coefficient -14? Let's list all of the factors of 24:\r<BR>\n" );
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document.write( "Factors of 24:\r<BR>\n" );
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document.write( "1,2,3,4,6,8,12,24\r<BR>\n" );
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document.write( "-1,-2,-3,-4,-6,-8,-12,-24 ...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 24\r<BR>\n" );
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document.write( "1*24\r<BR>\n" );
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document.write( "2*12\r<BR>\n" );
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document.write( "3*8\r<BR>\n" );
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document.write( "4*6\r<BR>\n" );
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document.write( "(-1)*(-24)\r<BR>\n" );
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document.write( "(-2)*(-12)\r<BR>\n" );
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document.write( "(-3)*(-8)\r<BR>\n" );
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document.write( "(-4)*(-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 -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\">24</TD><TD >1+24=25</TD></tr><tr><TD  align=\"center\">2</TD><TD  align=\"center\">12</TD><TD >2+12=14</TD></tr><tr><TD  align=\"center\">3</TD><TD  align=\"center\">8</TD><TD >3+8=11</TD></tr><tr><TD  align=\"center\">4</TD><TD  align=\"center\">6</TD><TD >4+6=10</TD></tr><tr><TD  align=\"center\">-1</TD><TD  align=\"center\">-24</TD><TD >-1+(-24)=-25</TD></tr><tr><TD  align=\"center\">-2</TD><TD  align=\"center\">-12</TD><TD >-2+(-12)=-14</TD></tr><tr><TD  align=\"center\">-3</TD><TD  align=\"center\">-8</TD><TD >-3+(-8)=-11</TD></tr><tr><TD  align=\"center\">-4</TD><TD  align=\"center\">-6</TD><TD >-4+(-6)=-10</TD></tr>\n" );
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document.write( "From this list we can see that -2 and -12 add up to -14 and multiply to 24\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=3s%5E2-14s%2B8 ALIGN=MIDDLE  ALT=\"3s%5E2-14s%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-14s ALIGN=MIDDLE  ALT=\"-14s\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2s%2B-12s ALIGN=MIDDLE  ALT=\"-2s%2B-12s\"   DISABLED_style= \"max-width:90%; height:auto;\" > (notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2s%2B-12s ALIGN=MIDDLE  ALT=\"-2s%2B-12s\"   DISABLED_style= \"max-width:90%; height:auto;\" > adds up to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-14s ALIGN=MIDDLE  ALT=\"-14s\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So it is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-14s ALIGN=MIDDLE  ALT=\"-14s\"   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=3s%5E2%2Bhighlight%28-2s%2B-12s%29%2B8 ALIGN=MIDDLE  ALT=\"3s%5E2%2Bhighlight%28-2s%2B-12s%29%2B8\"   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=3s%5E2-2s-12s%2B8 ALIGN=MIDDLE  ALT=\"3s%5E2-2s-12s%2B8\"   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=%283s%5E2-2s%29%2B%28-12s%2B8%29 ALIGN=MIDDLE  ALT=\"%283s%5E2-2s%29%2B%28-12s%2B8%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=s%283s-2%29-4%283s-2%29 ALIGN=MIDDLE  ALT=\"s%283s-2%29-4%283s-2%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=s ALIGN=MIDDLE  ALT=\"s\"   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=-4 ALIGN=MIDDLE  ALT=\"-4\"   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=%28s-4%29%283s-2%29 ALIGN=MIDDLE  ALT=\"%28s-4%29%283s-2%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=3s-2 ALIGN=MIDDLE  ALT=\"3s-2\"   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=3s%5E2-2s-12s%2B8 ALIGN=MIDDLE  ALT=\"3s%5E2-2s-12s%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28s-4%29%283s-2%29 ALIGN=MIDDLE  ALT=\"%28s-4%29%283s-2%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=3s%5E2-14s%2B8 ALIGN=MIDDLE  ALT=\"3s%5E2-14s%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28s-4%29%283s-2%29 ALIGN=MIDDLE  ALT=\"%28s-4%29%283s-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3s%5E2-14s%2B8 ALIGN=MIDDLE  ALT=\"3s%5E2-14s%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3s%5E2-2s-12s%2B8 ALIGN=MIDDLE  ALT=\"3s%5E2-2s-12s%2B8\"   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=3s%5E2-14s%2B8 ALIGN=MIDDLE  ALT=\"3s%5E2-14s%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28s-4%29%283s-2%29 ALIGN=MIDDLE  ALT=\"%28s-4%29%283s-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If you need more help, email me at <a  rel=nofollow HREF=\"mailto:jim_thompson5910@hotmail.com?Subject=I%20Need%20Algebra%20Help\">jim_thompson5910@hotmail.com</a>\r<BR>\n" );
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document.write( "Also, feel free to check out my tutoring <a  rel=nofollow HREF=\"http://www.freewebs.com/jimthompson5910/home.html\">website</a>. \r<BR>\n" );
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document.write( "Jim\r<BR>\n" );
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document.write( " </SPAN>\n" );
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