Let A be a smooth algebra over a perfect field k of characteristic p>0. This paper evaluates K_*(A[x]/(x^n),(x)) in terms of the big deRham-Witt complex of A. The result generalized the case A = k, which was treated in an earlier paper. We use this to evaluate the groups Nil_*(A[x]/(x^n)). The result again is given in terms of big deRham-Witt complexes. When A is a polynomial algebra the structure of these groups is completely known.