Find a polynomial $f(x)$ of degree 4 that has the following zeros. \[ 0,2 \text { (multiplicity } 2 \text { ), }-6 \] Leave your answer in factored form. \[ f(x)=\square \]

Step 1 ：The zeros of a polynomial are the values of x for which the polynomial equals zero. If a polynomial has a zero of multiplicity 2, it means that the factor corresponding to that zero is squared in the polynomial.

Step 2 ：So, to find a polynomial of degree 4 that has zeros at 0, 2 (with multiplicity 2), and -6, we can simply multiply the factors corresponding to these zeros.

Step 3 ：The factor corresponding to a zero x is (x - zero). Therefore, the polynomial is given by \(f(x) = x \cdot (x - 2)^2 \cdot (x + 6)\).

Step 4 ：We can leave the polynomial in this factored form as requested by the question.

Step 5 ：\(\boxed{f(x)=x(x-2)^2(x+6)}\)