Don’t wash your carrots until you’re ready to use them. Moisture is the enemy of long storage. Wet carrots get moldy and slimy faster than you can say “crudité platter.”
If your carrots come in a plastic bag, poke a few holes in it for airflow. Or better yet, wrap them in a dry kitchen towel and place them in a loosely closed bag. The towel soaks up extra moisture like a good friend.
Another trick: separate them from ethlyene-producing fruits like apples and bananas. Those fruits release a gas that makes carrots go from “crisp” to “bitter” in record time. Give them a little space.
I once kept a bag of whole carrots for five weeks by storing them in a glass jar with a little water, like flowers. They stayed crunchy for so long, I felt like a vegetable wizard.