Let the leading term of the polynomial, f(x), be axⁿ.
Examine the possibilities. n a x -> - ∞ x -> +∞ ------- ---- ----------- ------------ even a>0 f -> +∞ f -> +∞ Not true even a<0 f-> - ∞ f-> -∞ True odd a>0 f-> -∞ f-> +∞ Not true odd a<0 f-> +∞ f-> -∞ Not true
Answer: (a) the degree of the polynomial is even, and (b) the coefficient of the leading term is negative.
