Proving that a polynomial is irreducible over $\mathbb{Q}$

Question

How can I show that $f=t^4-8t^3/3+24t^2/9-32t/27+10/81$ is irreducible over $\mathbb{Q}$?

Answer 1

Result: Let $F$ be a field and $h$ be a nonzero element of $F$. If $hf(x)$ is irreducible over $F$ then $f$ is irreducible over $F$

Now consider $$81f(t)=81t^4-216t^3+216t^2-96t+10$$ By Eisenstein criterion with prime $p=2$, this polynomial is irreducible and hence $f$ is irreducible