The expression x^2 + 15x + 54 can be written as (x + a)(x + b), and the expression x^2 - 17x + 72 written as (x - b)(x - c), where a, b, and c are integers. What is the value of a+b+c?

x^{2} + 15x + 54 factors to (x + 6)(x + 9) a = 6 and b = 9

x^{2} – 17x + 72 factors to (x – 9)(x – 8) b = 9 and c = 8

so a + b + c = 6 + 9 + 8 = 23