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The growing market for Digital Signal Processing (DSP), Computer graphics and embedded systems applications that can be modeled as polynomial computations in their datapath designs, requires improvements in high-level synthesis and optimization techniques for such systems. This paper concentrates on how to find common sub-expressions between s given polynomial functions over Z2n1 × Z2n2 × … × Z2nd to Z2m in order to optimize the area and delay as much as possible. Our main contributions in this paper is proposing an optimization method based on adding/deleting vanishing polynomials over Z2m, i.e., those polynomials that are equivalent to zero over Z2m, to/from given polynomial functions in the hope of achieving further common sub-expressions. After applying our optimization techniques, experimental comparisons with the state-of-the-art techniques show an average improvement in the area by 36.80% with an average delay decrease of 2.41%. Regarding the comparison with our previous works, the area and delay are improved by 21.4% and 8.7% respectively. [ABSTRACT FROM PUBLISHER]