Use the rational zeros theorem to list all possible rational zeros of the following. \[ h(x)=-3 x^{3}-3 x^{2}-x-7 \] Be sure that no value in your list appears more than once. \( \square \) \( \pm \square \) \( \square \) \[ \square, \square, \]

To find all possible rational zeros of the polynomial \(h(x) = -3x^3 - 3x^2 - x - 7\), we begin by identifying the leading coefficient and the constant term. The leading coefficient is \(-3\) and the constant term is \(-7\). According to the rational zeros theorem, the possible rational zeros are given by the ratios of the factors of the constant term to the factors of the leading coefficient. Factors of \(-7\): \(\pm 1, \pm 7\) Factors of \(-3\): \(\pm 1, \pm 3\) Now, we create the list of all possible rational zeros: \[ \frac{\text{Factors of constant term}}{\text{Factors of leading coefficient}} = \pm \frac{1}{1}, \pm \frac{1}{3}, \pm \frac{7}{1}, \pm \frac{7}{3} \] This gives us the possible rational zeros: \(\pm 1, \pm \frac{1}{3}, \pm 7, \pm \frac{7}{3}\) In the requested format, the complete list of rational zeros is: \[ \pm 1, \pm \frac{1}{3}, \pm 7, \pm \frac{7}{3} \]