Assume: $$ f(x) = \sum_{i=0}^k a_i x^k$$ From the three linear system in the question, we can write: $$ \begin{bmatrix} 5 \\ 10 \\ 2 \\ 37 \end{bmatrix} = \begin{bmatrix} \alpha_0 & \alpha_1 2^1 & \alpha_2 2^2 & \alpha_3 2^3 &\alpha_4 2^4 \\ \alpha_0 & \alpha_1 3^1 & \alpha_2 3^2 & \alpha_3 3^3 &