P

Mathematically, we define this set to be programs $\Phi$ such that:

$$P = \left\{\Phi: C(\Phi) \in O(n^p), p \in \mathbb{Z}\right\}$$

This essentially means that $P$ are the set of algorithms which are Polynomial in the complexity measure. Usually, this is time, and hence, we say that the algorithm is in $P$-time.

Note, that although the theoretical aspiration is to distinguish the polynomial (easy) algorithms from the others, an algorithm which is $O(n^{10})$ is still quite slow. Usually, we like linear - $O(n)$ or quadratic - $O(n^2)$ algorithms.