Answer
$${\text{True}}$$
Work Step by Step
$$\eqalign{
& \mathop {\lim }\limits_{x \to \infty } \frac{{p\left( x \right)}}{{{e^x}}} = 0 \cr
& {\text{If }}p\left( x \right){\text{ is a polynomial, then the statement is true, because}} \cr
& {\text{at }}\infty {\text{ }}{e^x}{\text{ eventually overpowers the polynomial, so }}\frac{{p\left( x \right)}}{{{e^x}}} = 0 \cr} $$
