document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=143850>Question 143850</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Factor to make 2 binomials<BR>\n" );
document.write( "2x^2 + 5xy - 2y^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #104685 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=104685\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Looking at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B5xy-2y%5E2 ALIGN=MIDDLE  ALT=\"2x%5E2%2B5xy-2y%5E2\"   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=-2y%5E2 ALIGN=MIDDLE  ALT=\"-2y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > where the coefficients are 2 and -2 respectively.\r<BR>\n" );
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document.write( "Now multiply the first coefficient 2 and the last coefficient -2 to get -4. Now what two numbers multiply to -4 and add to the  middle coefficient 5? Let's list all of the factors of -4:\r<BR>\n" );
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document.write( "Factors of -4:\r<BR>\n" );
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document.write( "1,2,4\r<BR>\n" );
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document.write( "-1,-2,-4 ...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 -4\r<BR>\n" );
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document.write( "(1)*(-4)<BR>\n" );
document.write( "-2*2<BR>\n" );
document.write( "(-1)*(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 5? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 5\r<BR>\n" );
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document.write( "<th>First Number</th><th>Second Number</th><th>Sum</th>\r\n" );
document.write( "<tr><TD  align=\"center\">1</TD><TD  align=\"center\">-4</TD><TD >1+(-4)=-3</TD></tr>\r\n" );
document.write( "<tr><TD  align=\"center\">-2</TD><TD  align=\"center\">2</TD><TD >-2+(2)=0</TD></tr>\r\n" );
document.write( "<tr><TD  align=\"center\">-1</TD><TD  align=\"center\">4</TD><TD >-1+4=3</TD></tr>\r\n" );
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document.write( "None of these pairs of factors add to 5. So the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B5xy-2y%5E2 ALIGN=MIDDLE  ALT=\"2x%5E2%2B5xy-2y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > cannot be factored\r<BR>\n" );
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document.write( "Double check your book/worksheet to make sure that you have the correct problem. </SPAN>\n" );
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