A (real) polynomial of (integer) degree n is a function of the form p(x)=a_{n}x^{n}+a_{n-1}x^[n-1}+a_{n-2}x^{n-2}+cdots+a_{2}x^2+a_{1}x+a_{0}, where a_{n} != 0 (otherwise it wouldn't be degree n), and all the other a's are arbitrary real numbers (and they can be zero).
If n is even, then a_{n}>0 implies that y->+infty as x->pm infty and a_{n}<0 implies y->-infty as x->pm infty.
If n is odd, then a_{n}>0 implies that y->+infty as x->+ infty and y->-infty as x->-infty and a_{n}<0 implies that y->-infty as x->+ infty and y->+infty as x->-infty.
The values of the other coefficients are irrelevant for determining the end behavior.
