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. (I)

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To list all possible rational zeros of the polynomial $$ h(x) = -3x^3 - 3x^2 - x - 7 $$ using the **Rational Zero Theorem**, follow these steps:

1. **Identify the Constant Term and Leading Coefficient:**
   - **Constant Term (a₀):** $$-7$$
   - **Leading Coefficient (aₙ):** $$-3$$

2. **Determine the Factors:**
   - **Factors of the Constant Term ($$p$$):** $$\pm 1, \pm 7$$
   - **Factors of the Leading Coefficient ($$q$$):** $$\pm 1, \pm 3$$

3. **Form Possible Rational Zeros ($$\frac{p}{q}$$):**
   - Combine each factor of the constant term with each factor of the leading coefficient.
   - Simplify each fraction to its lowest terms.

4. **List All Possible Rational Zeros:**
   $$
   \pm 1, \pm \frac{1}{3}, \pm 7, \pm \frac{7}{3}
   $$

**Final List of Possible Rational Zeros:**
$$
-7,\ -\frac{7}{3},\ -1,\ -\frac{1}{3},\ \frac{1}{3},\ 1,\ \frac{7}{3},\ 7
$$

**Alternatively, expressed with ± notation:**
$$
\pm 1,\ \pm \frac{1}{3},\ \pm 7,\ \pm \frac{7}{3}
$$

These are all the possible rational zeros of the given polynomial according to the Rational Zero Theorem.

**Answer:**
All rational numbers ±1, ±1⁄3, ±7, and ±7⁄3 are possible zeros of h (x)
All possible rational zeros are ±1, ±1⁄3, ±7, and ±7⁄3.

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. (I)

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