Let p : R→ R be a non-constant polynomial, that is, for every x in R, p(x) = α0 + α1x+ ... + anx, with an + 0. Prove that, if n is even then lim→∞ p(x) = +∞ and limx→-∞ p(x) = +∞ when an > 0, and lim→∞ p(x) = · 0, and limÃ→∞ p(x) = −∞ and lim¸→-∞ p(x) = when an < 0 and n is odd.