To find the polynomial with the specified zeros -8 and 2, we can use the fact that if a polynomial has zeros at \( r_1 \) and \( r_2 \), it can be expressed in factored form as:
\[ y = k(x - r_1)(x - r_2) \]
In this case, the zeros are \( r_1 = -8 \) and \( r_2 = 2 \). Therefore, we can write:
\[ y = k(x + 8)(x - 2) \]
For simplicity, we can let \( k = 1 \):
\[ y = (x + 8)(x - 2) \]
Now, let's expand this:
\[ y = x^2 - 2x + 8x - 16 \] \[ y = x^2 + 6x - 16 \]
So, the polynomial we derived is
\[ y = x^2 + 6x - 16 \]
This corresponds to option C:
C: \( y = x^2 + 6x - 16 \)