What are the zeros of the function \(f(x) = 2(x - 4)(x + 1)\)?

To find the zeros of the function (f(x) = 2(x - 4)(x + 1)), we need to set the function equal to zero and solve for (x):

[

2(x - 4)(x + 1) = 0

]

A product is equal to zero if at least one of the factors is equal to zero. The two factors we need to set to zero are (x - 4) and (x + 1):

1. Setting (x - 4 = 0) gives (x = 4).

2. Setting (x + 1 = 0) gives (x = -1).

Thus, the values of (x) for which the function is zero are (x = 4) and (x = -1).

This means the zeros of the function are precisely those two values: (x = 4) and (x = -1). Selecting the answer that reflects these zeros shows an understanding of how to derive the zeros of polynomial functions based on their factors.

In contrast, other options do not contain both zeros or contain incorrect values that are not derived from the factors