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. an,

To find the possible rational zeros of the polynomial \( h(x) = -3x^3 - 3x^2 - x - 7 \), we apply the Rational Zeros Theorem. This theorem states that the possible rational zeros are given by the ratio of the factors of the constant term and the leading coefficient. The constant term here is -7, and the leading coefficient is -3. The factors of -7 are \( \pm 1, \pm 7 \), and the factors of -3 are \( \pm 1, \pm 3 \). Therefore, the possible rational zeros are: \[ \frac{\text{Factors of } -7}{\text{Factors of } -3} = \frac{\pm 1}{\pm 1}, \frac{\pm 1}{\pm 3}, \frac{\pm 7}{\pm 1}, \frac{\pm 7}{\pm 3} \] This leads us to several combinations, which simplify to the following possible rational zeros: \( \pm 1, \pm \frac{1}{3}, \pm 7, \pm \frac{7}{3} \). So, the complete list of potential rational zeros is: \( \pm 1, \pm \frac{1}{3}, \pm 7, \pm \frac{7}{3} \). Ensure that each value is considered only once, regardless of its sign.