There is no P in here, you can't solve for P without a P, Or I just don't get the question.
Answer: F (cos(230)).
Explanation:
Cosine corresponds to the x coordinate of points on a circle when the radius is drawn in like this, so the answer would be the cos of that angle, but you have to account for the fact that the 50 degree angle marked is just the reference angle not the entire angle so you have to add 180 degrees to that to get 230.
I didn't get all the part with the tiles, but here's the general answer:
given a polynomial
we have that 
is a factor of 
if and only if k is a root of , i.e. if
So, given the polynomial
We can check if 
is a factor by evaluating 
:
So, is not a factor.
Similarly, we can evaluate 
to check if 
are factors:
So, only 
is a factor of 
