Polynomials over bit-vectors, binary polynomials, are considered algebraically and it is observed that binary polynomials can be considered as a tree of subpolynomials. A construction of such subpolynomials is given. The application of these subpolynomials, along with other recent results on binary polynomials, in evaluating polynomials over bit-vectors as part of solving SMT problems is investigated. Preliminary results are given.