This work studies the zeros of slice functions over algebra dual quaternions and it comprises applications to problem factorizing motion polynomials. The class an alternative $*$-algebra $A$ was defined by Ghiloni Perotti in 2011, extending regular introduced Gentili Struppa 2006. Both classes strictly include polynomials $A$. We focus on case when is $\mathbb{DH}$. specific properties this all...