The problem of developing effective extrapolation methods is still relevant today, despite the existence of many known methods and approaches. In this paper, we consider the case of small samples of known data and the method of extrapolation based on the construction of the set of all possible polynomial forecasts. We present the results of the research concerning an algorithm for finding the optimal degree of the interpolation polynomial for solving the extrapolation problem. A number of important refinements of this algorithm are proposed. In particular, the procedure for building a forecast in the case when the convergence of a number of polynomial forecasts is non-monotonic has been clarified. We consider the case when the series of polynomial forecasts diverges. A detailed study of this case showed that an effective forecast can be constructed by averaging the first terms of a series of polynomial forecasts, provided there is no monotonicity. A stochastic case was also considered using the example of the Bitcoin exchange rate. Analysis of the polinomial predictive set showed that the criterion for choosing the number of consecutive values of a series of polynomial forecasts is the minimum deviation of the corresponding arithmetic mean to the last known value of the input time series. The proposed algorithms are important because they make it possible to build effective forecasts of various processes based on polynomials.