Show that the family $\left( L _ { 1 } , \ldots , L _ { n } \right)$ is an orthonormal basis of $\mathbb { R } _ { n - 1 } [ X ]$ equipped with the inner product $\langle \cdot , \cdot \rangle$.
Show that the family $\left( L _ { 1 } , \ldots , L _ { n } \right)$ is an orthonormal basis of $\mathbb { R } _ { n - 1 } [ X ]$ equipped with the inner product $\langle \cdot , \cdot \rangle$.