Based IRS' Qualifying Child test (see #3 below), your foster child is not a qualifying child and doesn't count as a dependent because the foster child didn't live with you for half of 2017 (Aug-Dec is 5 months).
According to the Internal Revenue
Service Publication 501, Exemptions,
Standard Deduction and Filing
Information, foster parents may be
eligible to claim a Dependent
Exemption for each child in foster care
they care for during the tax year who is
eligible to be considered a Qualifying
Child. IRS has certain tests to see if the foster child is a Qualifying Child.
What is a Qualifying Child?
A qualifying child is a child living in
your home who meets the 5 Internal
Revenue Service (IRS) tests/rules to
be considered a qualifying child. The
tests are:
1. Relationship (the child must
have been placed in your home by
the state or an approved agency
for you to foster)
2. Age (the child must be under
age 19 by the end of the tax year,
age 24 if a student or any age if
permanently disabled)
3. Residency (the child must have
lived with you for more than half of
the year)
Note: The time period must be
during the specific tax year
between January 1 and
December 31.
4. Support (the child cannot have
provided more than half of his or
her own support for the year)
Note: The foster care board rate
you receive is considered support
from the state - not from the child.
5. Joint Return (the child cannot
file a joint return)
If all five of these tests are met, the
child is considered to be a qualifying
child.
https://www.fafsonline.org/fact_sheets/claiming-dependent-exemption-foster-care.pdf
