Question 98
Given $a_{n} \in \mathbb{Z}$ with $a_{10}=11$ and $a_{9}=-143$, determine the number of polynomials of the form
$$
P(x)=\sum_{n=0}^{10} a_{n} x^{n}
$$
such that the zeros of $P(x)$ are all positive integers.
$$
P(x)=\sum_{n=0}^{10} a_{n} x^{n}
$$
such that the zeros of $P(x)$ are all positive integers.