Question 4
Find all polynomials $p(x)$ with real coefficients that have the following property: There exists a polynomial $q(x)$ with real coefficients such that
$$
p(1)+p(2)+p(3)+\cdots+p(n)=p(n) q(n)
$$
for all positive integers $n$.
$$
p(1)+p(2)+p(3)+\cdots+p(n)=p(n) q(n)
$$
for all positive integers $n$.