Let A be a commutative ring. A subset X of A^n is a polynomial family with d parameters if it is the range of a polynomial map from A^d to A^n. It is an old question of Skolem (1938) whether the group SL_2(A) with A being the set of integers is a polynomial family. Only recently, Vaserstein (2010) answered Skolem´s question in the affirmative. Along the way, he also shows that many arithmetic groups including the symplectic groups Sp_{2n}(\mathbb{Z}), the orthogonal groups SO_n(\mathbb{Z}), and the corresponding spinor groups Spin_n(\mathbb{Z}) are polynomial families. In this talk, I will discuss my recent result proving that SL_n(A) with n > 1 is a polynomial family, where A is the polynomial ring over a finite field of q elements. This is a function field analogue of Vaserstein´s theorem.