jmc

Question

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?

Accepted Answer

Factoring, we find that x^2 + 15x + 54 = (x + 9)(x + 6) and x^2 - 17x + 72 = (x - 9)(x - 8). We can see that b = 9, therefore a = 6 and c = 8, and a + b + c = 23.