Let L be a linear functional on the vector space of polynomials in x. Let $omega(x)$ be a polynomial in x of degree d, for some positive integer d. We consider two sets of polynomials, ${R_n (x)}_{n geq 0}, {S_n(x)}_{n geq 0}$, such that $R_n(x)$ is a polynomial in x of degree n and $S_n(x)$ is a polynomial in $omega(x)$ of degree n. (So $S_n(x)$ is a polynomial in x of degree dn.)