<PRE><B>Question 489173</B>
&lt;pre&gt;
3x&lt;sup&gt;5&lt;/sup&gt;+3x&lt;sup&gt;4&lt;/sup&gt;-18x&lt;sup&gt;3&lt;/sup&gt;+18x&lt;sup&gt;2&lt;/sup&gt;
The coefficients are 3,3,-18, and 18.  3 is the largest integer that
all of them are divisible by:

The variable parts are x&lt;sup&gt;5&lt;/sup&gt;, x&lt;sup&gt;4&lt;/sup&gt;, x&lt;sup&gt;3&lt;/sup&gt;, and x&lt;sup&gt;2&lt;/sup&gt;.  x&lt;sup&gt;2&lt;/sup&gt; is the largest
power that all of them will divide into. [It sounds contradictory
that &quot;the smallest is the largest&quot; but the smallest power is the
largest power that can be taken out]. 

So the greatest common factor GCF is 3x&lt;sup&gt;2&lt;/sup&gt;, and

3x&lt;sup&gt;2&lt;/sup&gt;(x&lt;sup&gt;3&lt;/sup&gt;+x&lt;sup&gt;2&lt;/sup&gt;-6x+6)

is the simplest factored form.


Edwin&lt;/PRE&gt;


</PRE>