document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=131049>Question 131049</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find one of the factors of: y^2+3y-40 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #95653 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=95653\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
document.write( "\n" );
document.write( "Looking at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1y%5E2%2B3y-40 ALIGN=MIDDLE  ALT=\"1y%5E2%2B3y-40\"   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=1y%5E2 ALIGN=MIDDLE  ALT=\"1y%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=-40 ALIGN=MIDDLE  ALT=\"-40\"   DISABLED_style= \"max-width:90%; height:auto;\" > where the coefficients are 1 and -40 respectively.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now multiply the first coefficient 1 and the last coefficient -40 to get -40. Now what two numbers multiply to -40 and add to the  middle coefficient 3? Let's list all of the factors of -40:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Factors of -40:\r<BR>\n" );
document.write( "\n" );
document.write( "1,2,4,5,8,10,20,40\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-1,-2,-4,-5,-8,-10,-20,-40 ...List the negative factors as well. This will allow us to find all possible combinations\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "These factors pair up and multiply to -40\r<BR>\n" );
document.write( "\n" );
document.write( "(1)*(-40)\r<BR>\n" );
document.write( "\n" );
document.write( "(2)*(-20)\r<BR>\n" );
document.write( "\n" );
document.write( "(4)*(-10)\r<BR>\n" );
document.write( "\n" );
document.write( "(5)*(-8)\r<BR>\n" );
document.write( "\n" );
document.write( "(-1)*(40)\r<BR>\n" );
document.write( "\n" );
document.write( "(-2)*(20)\r<BR>\n" );
document.write( "\n" );
document.write( "(-4)*(10)\r<BR>\n" );
document.write( "\n" );
document.write( "(-5)*(8)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "note: remember, the product of a negative and a positive number is a negative number\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now which of these pairs add to 3? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<TABLE  border=\"1\">\n" );
document.write( "<th>First Number</th><th>Second Number</th><th>Sum</th><tr><TD  align=\"center\">1</TD><TD  align=\"center\">-40</TD><TD >1+(-40)=-39</TD></tr><tr><TD  align=\"center\">2</TD><TD  align=\"center\">-20</TD><TD >2+(-20)=-18</TD></tr><tr><TD  align=\"center\">4</TD><TD  align=\"center\">-10</TD><TD >4+(-10)=-6</TD></tr><tr><TD  align=\"center\">5</TD><TD  align=\"center\">-8</TD><TD >5+(-8)=-3</TD></tr><tr><TD  align=\"center\">-1</TD><TD  align=\"center\">40</TD><TD >-1+40=39</TD></tr><tr><TD  align=\"center\">-2</TD><TD  align=\"center\">20</TD><TD >-2+20=18</TD></tr><tr><TD  align=\"center\">-4</TD><TD  align=\"center\">10</TD><TD >-4+10=6</TD></tr><tr><TD  align=\"center\">-5</TD><TD  align=\"center\">8</TD><TD >-5+8=3</TD></tr>\n" );
document.write( "</TABLE>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "From this list we can see that -5 and 8 add up to 3 and multiply to -40\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now looking at the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1y%5E2%2B3y-40 ALIGN=MIDDLE  ALT=\"1y%5E2%2B3y-40\"   DISABLED_style= \"max-width:90%; height:auto;\" >, replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y ALIGN=MIDDLE  ALT=\"3y\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5y%2B8y ALIGN=MIDDLE  ALT=\"-5y%2B8y\"   DISABLED_style= \"max-width:90%; height:auto;\" > (notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5y%2B8y ALIGN=MIDDLE  ALT=\"-5y%2B8y\"   DISABLED_style= \"max-width:90%; height:auto;\" > adds up to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y ALIGN=MIDDLE  ALT=\"3y\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So it is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y ALIGN=MIDDLE  ALT=\"3y\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1y%5E2%2Bhighlight%28-5y%2B8y%29%2B-40 ALIGN=MIDDLE  ALT=\"1y%5E2%2Bhighlight%28-5y%2B8y%29%2B-40\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now let's factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1y%5E2-5y%2B8y-40 ALIGN=MIDDLE  ALT=\"1y%5E2-5y%2B8y-40\"   DISABLED_style= \"max-width:90%; height:auto;\" > by grouping:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281y%5E2-5y%29%2B%288y-40%29 ALIGN=MIDDLE  ALT=\"%281y%5E2-5y%29%2B%288y-40%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group like terms\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%28y-5%29%2B8%28y-5%29 ALIGN=MIDDLE  ALT=\"y%28y-5%29%2B8%28y-5%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=y ALIGN=MIDDLE  ALT=\"y\"   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=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" > out of the second group\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2B8%29%28y-5%29 ALIGN=MIDDLE  ALT=\"%28y%2B8%29%28y-5%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=y-5 ALIGN=MIDDLE  ALT=\"y-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can combine like terms\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1y%5E2-5y%2B8y-40 ALIGN=MIDDLE  ALT=\"1y%5E2-5y%2B8y-40\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2B8%29%28y-5%29 ALIGN=MIDDLE  ALT=\"%28y%2B8%29%28y-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So this also means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1y%5E2%2B3y-40 ALIGN=MIDDLE  ALT=\"1y%5E2%2B3y-40\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2B8%29%28y-5%29 ALIGN=MIDDLE  ALT=\"%28y%2B8%29%28y-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1y%5E2%2B3y-40 ALIGN=MIDDLE  ALT=\"1y%5E2%2B3y-40\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1y%5E2-5y%2B8y-40 ALIGN=MIDDLE  ALT=\"1y%5E2-5y%2B8y-40\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "     Answer:\r<BR>\n" );
document.write( "\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2B3y-40 ALIGN=MIDDLE  ALT=\"y%5E2%2B3y-40\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2B8%29%28y-5%29 ALIGN=MIDDLE  ALT=\"%28y%2B8%29%28y-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that one of factors are either <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B8 ALIGN=MIDDLE  ALT=\"y%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-5 ALIGN=MIDDLE  ALT=\"y-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );