Polynomials over a Field · Challenge problem

$x^4+x+1$ factors, so $x^4+x+5$ factors

Nothing: mod $2$ tests only work for cubics

$x^4+x+5$ has a rational root

$x^4+x+1$ is irreducible over $\mathbb Z_2$, so $x^4+x+5$ is irreducible over $\mathbb Q$