Final answer:
The value of c that makes the expression x^2 + 28x + c a perfect-square trinomial is 196, since the square of half the coefficient of x (which is 14) gives c.
Step-by-step explanation:
To determine the value of c such that the expression x^2 + 28x + c is a perfect-square trinomial, we need to follow a mathematical methodology. A perfect-square trinomial takes the form (x + a)^2 = x^2 + 2ax + a^2. In this case, we have the middle term which is 28x, hence 2a must be 28 leading to a being 14. Therefore, the term a^2, which gives us the value of c, is 14^2 which equals 196. So, the correct answer is b) c = 196.