What is a cubic polynomial function in standard form with zeros $1,-2$, and $2 ?$ (1 point) $f(x)=x^{3}+x^{2}-3 x+4$ $f(x)=x^{3}+x^{2}-4 x-2$ $f(x)=x^{3}+x^{2}+4 x+4$ $f(x)=x^{3}-x^{2}-4 x+4$

Step 1 ：The standard form of a cubic polynomial function with zeros a, b, and c is \(f(x) = k(x-a)(x-b)(x-c)\), where k is a constant.

Step 2 ：In this case, the zeros are 1, -2, and 2, so the function is \(f(x) = k(x-1)(x+2)(x-2)\).

Step 3 ：We don't know the value of k, but since it's not specified in the question, we can assume k=1.

Step 4 ：Substituting the values of a, b, and c into the equation, we get \(f(x) = (x - 1)(x + 2)(x - 2)\).

Step 5 ：Expanding this equation, we get \(f(x) = x^{3}-x^{2}-4 x+4\).

Step 6 ：Final Answer: The cubic polynomial function in standard form with zeros 1,-2, and 2 is \(\boxed{f(x)=x^{3}-x^{2}-4 x+4}\).