Edwin's solution.
Stanbon is right. You are finding the horizontal asymptote.  Here's
a little more detailed way to look at it. 

 lim 
x->OO 


Finding the limit of a rational function as x approaches infinity depends
on this theorem that we accept on faith:

limx->oo = 0, if n>0 and k is any constant.

Method: Divide every term on top and bottom of 
by the largest power of x that appears in there.

So,

limx->oo 

becomes

limx->oo 

and upon simplifying the fractions, you have:

limx->oo

Now every term on top approaches 0 as x approaches infinity.
So the whole numerator approaches 0.  

And the two terms of the denominator other than the 8 both
approack 0, and so, the fraction approaches  

So the limit is 0.

Note:
[Note here that the denominator did not approach 
0 too, and we were saved from having to face that dilemma 
of having both a numerator and a denominator approach 0.
But that dilemma occurs in other problems you'll be studying.]

Edwin