Question

Select ALL the zeros of the following polynomial function. f(x) = (x - 3)(x + 2)(x - 4)

Options:
A. -4
B. -3
C. -2
D. 2
E. 3
F. 4

Answer 1

The zeros of the polynomial function f(x) = (x - 3)(x + 2)(x - 4) are -2, 3, and 4, which correspond to options C, E, and F.

Step-by-step explanation:

The zeros of a polynomial function are the values of x that make the function equal to zero. For the polynomial function given, f(x) = (x - 3)(x + 2)(x - 4), we find the zeros by setting each factor equal to zero.

If we set (x - 3) = 0, we find that x = 3. So, 3 is a zero of the function, corresponding to option E.

Setting (x + 2) = 0 gives us x = -2, identifying -2 as another zero of the function, corresponding to option C.

Finally, by setting (x - 4) = 0, we get x = 4, which reveals that 4 is the last zero, corresponding to option F.

The polynomial function is given by f(x) = (x - 3)(x + 2)(x - 4). To find the zeros of the function, we need to set the function equal to zero and solve for x.

Setting the function equal to zero:

(x - 3)(x + 2)(x - 4) = 0

Using the zero product property, we know that the equation is satisfied when any one of the factors is equal to zero. So, the zeros of the polynomial function are:

x = 3

x = -2

x = 4

Therefore, the zeros of the polynomial function are -2, 3, and 4.