Algebra-1

The correct answer is C. f(x) = (x - 2)(x + 6)(x - 5) is the function that has roots at -6, 2, and 5.

To determine which of the given functions has roots at -6, 2, and 5, we need to substitute these values into each function and check if they result in f(x) being equal to zero.

Option A:
f(x) = (x + 2)(x + 6)(x + 5)
When we substitute x = -6, we get: f(-6) = (-6 + 2)(-6 + 6)(-6 + 5) = -4 * 0 * -1 = 0.
When we substitute x = 2, we get: f(2) = (2 + 2)(2 + 6)(2 + 5) = 4 * 8 * 7 = 224.
When we substitute x = 5, we get: f(5) = (5 + 2)(5 + 6)(5 + 5) = 7 * 11 * 10 = 770.
Option A does not satisfy the condition, as f(-6) ≠ 0. Therefore, it does not have the roots at -6, 2, and 5.

Option B:
f(x) = (x + 2)(x - 6)(x - 5)
When we substitute x = -6, we get: f(-6) = (-6 + 2)(-6 - 6)(-6 - 5) = -4 * -12 * -11 = -528.
When we substitute x = 2, we get: f(2) = (2 + 2)(2 - 6)(2 - 5) = 4 * -4 * -3 = 48.
When we substitute x = 5, we get: f(5) = (5 + 2)(5 - 6)(5 - 5) = 7 * -1 * 0 = 0.
Option B does not satisfy the con...