$\{\phi_1, \phi_2,...\}$ are orthogonal polynomials with respect to some arbitrary real inner product but are normalised to be monic. The question doesnt say but I think $\phi_i$ is supposed to be of degree exactly $i$
If $p$ is any polynomial of degree $k$ show that $\|\phi_k\| \leq \|p\|$. (The norm induced from this inner product)
Edit: $p$ must be monic