My husband and I have a 19 yr old daughter who goes to college in another State (California ), she has a scholarship that covers her tuition fees. She worked part time which paid for half of her dorm

If she was a full-time student for at least five months during 2019 and she did not provide more than half of her own support, then you meet the requirements. Her time away at college is considered a temporary absence and counts as time spent in your home. She may also file her own return but must indicate that she is being claimed as a dependent. You can use the IRS Worksheet for Determining Support if you need help in determining if she has paid more than half.

Yes, you can claim her as a dependent* and claim the Tuition credit for her education**.  Be sure she knows that you are claiming her, so that she checks the box on her form that say she is being claimed as a dependent.

With the tax law change, effective 2018, most students will get the same refund whether they claim themselves or not. The personal exemption has been eliminated and the standard deduction increased.

*A child of a taxpayer can still be a “Qualifying Child” (QC) dependent, regardless of his/her income, if:

1. He is under age 19, or under 24 if a full time student for at least 5 months of the year, or is totally & permanently disabled
2. He did not provide more than 1/2 his own support. Scholarships are considered third party support and not as support provided by the student.
3. He lived with the parent (including temporary absences such as away at school) for more than half the year

So, it doesn't matter how much he earned. What matters is how much he spent on support. Money he put into savings does not count as support he spent on him self.

The support value of the home, provided by the parent, is the fair market rental value of the home plus utilities & other expenses divided by the number of occupants.

**The tuition credit goes with the student's dependency, regardless of who paid it. Furthermore, most students are not eligible for the refundable portion of the American Opportunity Credit.   It is usually best if the parent claims that credit.