To add to VincentL's great post, I would note that whether you can claim the child as a dependent is up to you and the child's other parent.
With the child only staying with you for 8 nights a month, you do not qualify as the custodial parent by the IRS definition. However, you might have or make an agreement with the other parent to allow you to claim the child as a dependent even when you're not the custodial parent. That's totally up to whatever you negotiated or can agree upon - often the question of claiming the child will be addressed in a divorce or custody/parenting agreement.
**Say "Thanks" by clicking the thumb icon in a post
**Mark the post that answers your question by clicking on "Mark as Best Answer"
