document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=725381>Question 725381</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Factor if possible<BR>\n" );
document.write( "5x^2-20x-xy+4y<BR>\n" );
document.write( "thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #444207 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=444207\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The greatest common factor (GCF) us 1 (which we rarely bother factoring out). There are too many terms for factoring patterns or for trinomial factoring. So we'll try factoring by grouping.<br><BR>\n" );
document.write( "Since factoring by grouping requires grouping (obviously) and sometime reordering the terms, I like to rewrite the expression as additions so that I can do both freely:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2%2B%28-20x%29%2B%28-xy%29%2B4y ALIGN=MIDDLE  ALT=\"5x%5E2%2B%28-20x%29%2B%28-xy%29%2B4y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we group the expression into two halves:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x%5E2%2B%28-20x%29%29%2B%28%28-xy%29%2B4y%29 ALIGN=MIDDLE  ALT=\"%285x%5E2%2B%28-20x%29%29%2B%28%28-xy%29%2B4y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then we factor out the GCF of each group. Two important notes:<ul><li>This point in factoring by grouping is one of those rare times when we actually <i>do</i> factor out a GCF of 1!</li><li>If the first terms of the two groups have opposite signs, then factor out the negative of the GCF <i>from one of the groups</i>.</li></ul>The GCF of the first group is 5x. The GCF of the second group is y. But since the first term of the two groups have different signs, we will factor out -y from the second group:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%28x%2B%28-4%29%29%2B%28-y%29%28x%2B%28-4%29%29 ALIGN=MIDDLE  ALT=\"5x%28x%2B%28-4%29%29%2B%28-y%29%28x%2B%28-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If we're lucky, the two \"non-GCF\" factors of the two groups will match. With (x+(-4)) in both groups we got lucky. (If we didn't get lucky then we would have to start over, try a different order and different grouping and repeat this until we get lucky or we figure out that factoring by grouping will just not work.) Factoring out the common factor of (x+(-4)) we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B%28-4%29%29%285x%2B%28-y%29%29 ALIGN=MIDDLE  ALT=\"%28x%2B%28-4%29%29%285x%2B%28-y%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which should be an acceptable answer. Or you could change back to subtractions:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%285x-y%29 ALIGN=MIDDLE  ALT=\"%28x-4%29%285x-y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );