It goes the same for most of root vegetables such as swede (kålrot,) celery root, parsnip (pastinakk,) turnip (nepe), Daikon (Japanese reddik) etc..
If they are kept in plastic, please make sure they are dry. The water tends to make them rot faster. Thus, it's wise to wrap them in newspaper or advertisement paper (but not with the shiny coating on the surface of the paper. It's important that they absorb water...) or kitchen paper, then keep them in plastic bag, and store in fridge.
During summer, we can buy carrots with green stems. After purchasing them, please remove the stems - the carrots will keep longer by removing them.
There are two ways of freezing carrots. They can be peeled and chopped, and frozen as they are, or peeled, chopped, and blanched before freezing.
Blanching would stop enzymes which decays vegetables. The easiest way of blanching is to place carrot pieces in a bowl, pour boiling water, and drain the water.