Algebra-1

The correct answer is C. f(x) = (x + 4)(x - 8)(x + 2) is the function that has roots at 8, -2, and -4.

To determine which of the given functions has roots at 8, -2, and -4, 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 - 4)(x + 8)(x + 2)
When we substitute x = -8, we get: f(-8) = (-8 - 4)(-8 + 8)(-8 + 2) = -12 * 0 * -6 = 0.
When we substitute x = -2, we get: f(-2) = (-2 - 4)(-2 + 8)(-2 + 2) = -6 * 6 * 0 = 0.
When we substitute x = 4, we get: f(4) = (4 - 4)(4 + 8)(4 + 2) = 0 * 12 * 6 = 0.
Option A satisfies the condition and has roots at -8, -2, and 4.

Option B:
f(x) = (x + 4)(x + 8)(x + 2)
When we substitute x = -8, we get: f(-8) = (-8 + 4)(-8 + 8)(-8 + 2) = -4 * 0 * -6 = 0.
When we substitute x = -2, we get: f(-2) = (-2 + 4)(-2 + 8)(-2 + 2) = 2 * 6 * 0 = 0.
When we substitute x = 4, we get: f(4) = (4 + 4)(4 + 8)(4 + 2) = 8 * 12 * 6 = 576.
Option B does not satisfy the condition, a...