You have two sources of information:
1) F(x) = ax^2 + bx + c (a general definition of the polynomial F(x)).
From it, a + b + c = F(1).
2) You also are given the second piece of information: F(x+5) = x^2 + 9x - 7.
To get F(1), you need to take x = -4 in the last identity, and then you will get
a + b + c = F(1) = F(-4 + 5) = (-4)^2 + 9*(-4) - 7 = 16 - 36 - 7 = -27.
ANSWER. a + b + c = -27.
Solved.
-----------------
This problem is good for an interview, if the company wants to hire someone with creative mathematical mind.
If the interviewed person solves it in this way, he (or she) deserves the " + " sign in the answer list.
If he (or she) will solve it by another way (by direct substituting and manipulating coefficients), he (or she) deserves " - "
(even if he (or she) will get a correct answer finally).
