To find a polynomial that has zeros at \( x = -2 \), \( x = 0 \), \( x = 3 \), and \( x = 5 \), we can write it in factored form based on its zeros:
The factors corresponding to the given zeros are:
- \( (x + 2) \) for the zero at \( x = -2 \)
- \( (x - 0) \) or simply \( x \) for the zero at \( x = 0 \)
- \( (x - 3) \) for the zero at \( x = 3 \)
- \( (x - 5) \) for the zero at \( x = 5 \)
Therefore, the polynomial can be written as:
\[ y = (x + 2)(x)(x - 3)(x - 5) \]
Now, let's analyze the answer choices provided:
- \( y = x(x + 2)(x - 3)(x - 5) \) - This includes all zeros, which includes the correct factors.
- \( y = (x + 2)(x - 3)(x - 5) \) - This does not include the zero at \( x = 0 \).
- \( y = (x - 2)(x - 3)(x - 5) \) - This does not have any of the correct zeros specified.
- \( y = (x - 2)(x + 3)(x + 5) \) - This also does not match any of the specified zeros.
Among the choices, the only polynomial that correctly represents the given zeros is:
\[ \boxed{y = x(x + 2)(x - 3)(x - 5)} \]