document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=126457>Question 126457</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (x+1)(x+2)(x+3)(x+4) = 120 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #92643 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=92643\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An analytical way of doing this problem is to look at the factors of 120.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Divide it by 2 and you get 60*2<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Divide the 60 by 4 to get 4 and 15 as factors of 60 and you have that the factors of 120<BR>\n" );
document.write( "have become 4*15*2.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Then factor 15 into 5*3 and substitute that result for 15 to get that the factors of 120 <BR>\n" );
document.write( "are 4*3*5*2. If you multiply these factors together you do get 120, so our factors check out<BR>\n" );
document.write( "to be OK.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now arrange the factors in ascending order: 2*3*4*5<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Notice significantly that each of these factors increases by 1. Now compare them to the<BR>\n" );
document.write( "factors on the left side of the problem you were given ...<BR>\n" );
document.write( ".<BR>\n" );
document.write( "(x+1)*(x+2)*(x+3)*(x+4)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Each of those factors is 1 greater than the preceding factor ... and there are four of them<BR>\n" );
document.write( "just as we found in the four factors 2*3*4*5<BR>\n" );
document.write( ".<BR>\n" );
document.write( "What do we get if we set  the first factor x + 1  equal to 2 ... we find x = 1<BR>\n" );
document.write( ".<BR>\n" );
document.write( "What do we get if we set the second factor x + 2 equal to 3 ... we again find x = 1<BR>\n" );
document.write( ".<BR>\n" );
document.write( "What do we get if we set the third factor x + 3 equal to 4 ... we again find x = 1<BR>\n" );
document.write( ".<BR>\n" );
document.write( "And, finally, what do we get if we set the fourth factor x + 4 equal to 5 ... we again find x = 1<BR>\n" );
document.write( ".<BR>\n" );
document.write( "What an interesting outcome. If in each of the four factors:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "(x+1)*(x+2)*(x+3)*(x+4)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "we set x = 1, the factors become 2*3*4*5 and this product is 120. So the solution <BR>\n" );
document.write( "to this problem is x = 1<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Sure was a lot easier to do it this way than to try multiplying out the 4 original factors<BR>\n" );
document.write( "and then setting that product equal to 120 and trying to solve that fourth order equation.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope this is clear enough so that you can follow it through and see what was done to solve<BR>\n" );
document.write( "the problem.<BR>\n" );
document.write( ".<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );