document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=848214>Question 848214</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am in the process of learning factorization of monomials.<BR>\n" );
document.write( "The Largest Common Factor is somewhat confusing for me.  How do you find the correct LCF when there is an exponent?<BR>\n" );
document.write( "Example:\r<BR>\n" );
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document.write( "24x^5y^2 + 18x^4y^6 - 30x^6y^4  \r<BR>\n" );
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document.write( "I know that 6 would be the LCF, how do I know about the exponent?\r<BR>\n" );
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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 #510950 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><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/cgi-bin/show-face.mpl?user=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=510950\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> By finding the GCF (or as you call it LCF) we isolate what is common in all of the terms.\r<BR>\n" );
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document.write( "Let's look at just the first two terms and break them down according to their prime factorization.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%282%29%2A2%2A2%2Ahighlight%283%29%2Ahighlight%28x%2Ax%2Ax%2Ax%29%2Ax%2Ahighlight%28y%2Ay%29 ALIGN=MIDDLE   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=highlight%282%29%2Ahighlight%283%29%2A3%2Ahighlight%28x%2Ax%2Ax%2Ax%29%2Ahighlight%28y%2Ay%29%2Ay%2Ay%2Ay%2Ay ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So we can see that 2*3*x*x*x*x*y*y is our LCF or  6*x^4*y^2 for the first two terms. We now try this with all 3.\r<BR>\n" );
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document.write( "24x^5y^2 + 18x^4y^6 - 30x^6y^4 \r<BR>\n" );
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document.write( "What we did before was the long way, but I think it will help you see what is going on.\r<BR>\n" );
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document.write( "What is in common with 24,18,30?  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%286%29 ALIGN=MIDDLE  ALT=\"highlight%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. That's part of our factor.\r<BR>\n" );
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document.write( "What is in common with x^5, x^4, x^6? <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x%5E4%29 ALIGN=MIDDLE  ALT=\"highlight%28x%5E4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > [they all contain at least 4 xs.]\r<BR>\n" );
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document.write( "What is in common with y^2, y^6, y^4? <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y%5E2%29 ALIGN=MIDDLE  ALT=\"highlight%28y%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > [they all contain at least 2 ys.]\r<BR>\n" );
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document.write( "So our final answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%286x%5E4y%5E2%29 ALIGN=MIDDLE  ALT=\"highlight%286x%5E4y%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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