\( 1 \leftarrow \begin{array}{l}\begin{array}{l}\text { Find a polynomial function of lowest degree } \\ \text { with rational coefficients that has the given } \\ \text { numbers as some of its zeros. }\end{array} \\ -2 i, 6\end{array} \)

To find the polynomial function of the lowest degree with rational coefficients and the given zeros \(-2i\) and \(6\), we must include the conjugate of the complex zero. Therefore, the zeros of the polynomial will be \(-2i\), \(2i\), and \(6\). The polynomial can be constructed by forming factors from these zeros: \[ f(x) = (x - 6)(x - (-2i))(x - 2i) \] This simplifies to: \[ f(x) = (x - 6)(x + 2i)(x - 2i) \] The product \((x + 2i)(x - 2i)\) yields \(x^2 + 4\). Thus, the polynomial becomes: \[ f(x) = (x - 6)(x^2 + 4) = x^3 - 6x^2 + 4x - 24 \] This gives you the polynomial function of the lowest degree with rational coefficients that has \(-2i\) and \(6\) as zeros: \[ f(x) = x^3 - 6x^2 + 4x - 24 \]