If p − 1 is a factor of p4 + p2 + p − k, the value of k is

It's says p-1 is factor to the equation, so that means when
p=1, the remeinder of the equation is zero. Mening:

p4 + p2 + p - k = 0

plug p=1 into the equation and find k

1^4 + 1^2 + 1 - k = 0
1 + 1 + 1 - k = 0
k = 3

The method to find the female dormitory is 2-d=800

Ithink the answer is discovery verbs because they are quite similar to the verb 'discovering'