Questions: Find the zeros of the polynomial function and state the multiplicity of each. f(x) = -2(x-2)^4(x+4)^2 x^3 The zero 2 has multiplicity .

Find the multiplicity of the zero 2 in the polynomial function \( f(x) = -2(x-2)^{4}(x+4)^{2}x^{3} \).

Identify the factor corresponding to the zero 2.

The factor corresponding to the zero 2 is \( (x-2) \).

Determine the exponent of the factor \( (x-2) \).

The exponent of \( (x-2) \) is 4.

State the multiplicity of the zero 2.

The multiplicity of the zero 2 is equal to the exponent of its corresponding factor, which is 4.

The zero 2 has multiplicity \(\boxed{4}\).

The zero 2 has multiplicity \(\boxed{4}\).