Unit testing MVP pattern with other pattern

I am implementing an application using MVP pattern. In my model, if i had to use factory pattern for some reason. How would I perform unit testing? Should I do unit testing on factory pattern as well or testing on my presenter should be enough?

Example:

In my model layer, I have to implement a package. The package will contain bunch of tasks. Each tasks will contain at least 1 person assign to it. For this scenario, I am using COMPOSITE PATTERN.

My question is, performing testing on the presenter is enough or I have to perform unit testing on composite pattern as well?