Irreducible polynomials of degree $d$ such that $[x]$ generates $\mathbf{F}_{p^d}^{\times}$

Question

It is often convenient to represent the field $\mathbf{F}_{p^d}$ as $\mathbf{F}_p[x]/(f(x))$, where $f$ is irreducible with degree $d$, $f$ has just a few nonzero terms, and $[x]$ itself is the generator of the multiplicative group $\mathbf{F}_{p^d}^{\times}$. How can we show that such polynomials for which $[x]$ is a cyclic generator and such that the polynomial is sparse exist, and how can we efficiently find them?