I was wondering if someone could show me how to do this.

I need to use this fact,

Let p(x) be a polynomial of degree n: p(x) = a0 + a1x + a2x^2 + · · · + anx^n (an cannot equal 0). The limit from x to infinity of p(x)/anx^n is 1 and the limit from x to negative infinity of p(x)/anx^n is 1

to prove that every real polynomial of odd degree has a real zero. I'm not really sure what to do and I would appreciate any help. Thanks in advance.