  Let $\mathcal{P}_{K} (^{n}E; F)$ (resp. $\mathcal{P}_{w} (^{n}E; F)$) the
subspace of all $P\in \mathcal{P}(^{n}E; F)$ which are compact (resp. weakly
continuous on bounded sets). We show that if $\mathcal{P}_{K} (^{n}E; F)$
contains an isomorphic copy of $c_{0}$, then $\mathcal{P}_{K} (^{n}E; F)$ is
not complemented in $\mathcal{P}(^{n}E; F)$. Likewise we show that if
$\mathcal{P}_{w} (^{n}E; F)$ contains an isomorphic copy of $c_{0}$, then
$\mathcal{P}_{w}(^{n}E; F)$ is not complemented in $\mathcal{P}(^{n}E; F)$.
