We prove that extendible 2-homogeneous polynomials on spaces with cotype 2 are integral. This allows us to find examples of approximable non-extendible polynomials on ${\ell }_p$ (1 ≤ p < ∞ ) of any degree. We also exhibit non-nuclear extendible polynomials for 4 < p < ∞. We study the extendibility of analytic functions on Banach spaces and show the existence of functions of infinite radius of convergence whose coefficients are finite type polynomials but which fail to be extendible.

We show that a Banach space X is an ℒ₁-space (respectively, an ${ℒ}_{\infty }$-space) if and only if it has the lifting (respectively, the extension) property for polynomials which are weakly continuous on bounded sets. We also prove that X is an ℒ₁-space if and only if the space ${}_{wb}{(}^{m}X)$ of m-homogeneous scalar-valued polynomials on X which are weakly continuous on bounded sets is an ${ℒ}_{\infty }$-space.