Infinite Families of $A_4$-Sextic Polynomials In this article we develop a test to determine whether a sextic polynomial that is irreducible over $\mathbb{Q}$ has Galois group isomorphic to the alternating group $A_4$. This test does not involve the computation of resolvents, and we use this test to construct several infinite families of such polynomials. Keywords:Galois group, sextic polynomial, inverse Galois theory, irreducible polynomialCategories:12F10, 12F12, 11R32, 11R09