1. The problem is to find the Lagrange polynomial that interpolates a given set of points. 2. The formula for the Lagrange polynomial of degree $n$ given points $(x_0,y_0), (x_1,y_1), \ldots, (x_n,y_n)$ is: $$L(x) = \sum_{j=0}^n y_j \ell_j(x)$$ where each basis polynomial $\ell_j(x)$ is defined as: $$\ell_j(x) = \prod_{\substack{0 \le m \le n \\ m \neq j}} \frac{x - x_m}{x_j - x_m}$$ 3. This formula constructs a polynomial that passes exactly through all given points by weighting each $y_j$ with a polynomial $\ell_j(x)$ that is 1 at $x_j$ and 0 at all other $x_m$. 4. To find the polynomial, you substitute the known points into the formula, compute each $\ell_j(x)$, and sum the terms. 5. Without specific points, the general form is as above. If you provide points, I can compute the explicit polynomial.