If $\mu_{p}(k)={1}$, $p$ is a prime, is the polynomial $\sum_{j=0}^{p-1}x^{j}$ irreducible over $k$?

Question

Suppose $k$ is a field and $p$ a prime. Assume that $\mu_{p}(k)={1}$, where $\mu_{p}$ denotes the group of $p^{\text{th}}$ roots of unity. Is the polynomial \begin{equation*} P(x)=\sum_{j=0}^{p-1}x^{j} \end{equation*} irreducible over $k$?