  The main purpose of this paper is to prove some density results of
polynomials in Fock spaces of slice regular functions. The spaces can be of two
different kinds since they are equipped with different inner products and
contain different functions. We treat both the cases, providing several
results, some of them based on constructive methods which make use of the
Taylor expansion and of the convolution polynomials. We also prove quantitative
estimates in terms of higher order moduli of smoothness and in terms of the
best approximation quantities.
