Use the Rational Zero Theorem to list all possible rational zeros of the given pol the $$ \pm $$ symbol and separate your answers with a comma. For example : $$ \pm 1, \pm 2 $$ $$ p(x)=x^{5}+17 x^{4}+7 x^{3}-12 x^{2}+x+36 $$

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To list all possible rational zeros of the polynomial $$ p(x) = x^{5} + 17x^{4} + 7x^{3} - 12x^{2} + x + 36 $$ using the **Rational Zero Theorem**, follow these steps:

1. **Identify the Leading Coefficient and Constant Term:**
   - **Leading Coefficient (aₙ):** The coefficient of the highest degree term, which is $$ 1 $$ (from $$ x^5 $$).
   - **Constant Term (a₀):** The constant term, which is $$ 36 $$.

2. **Determine Possible p and q Values:**
   - **p (factors of the constant term):** $$ \pm1, \pm2, \pm3, \pm4, \pm6, \pm9, \pm12, \pm18, \pm36 $$.
   - **q (factors of the leading coefficient):** Since the leading coefficient is $$ 1 $$, the only factor is $$ \pm1 $$.

3. **Form Possible Rational Zeros (p/q):**
   - Since $$ q = \pm1 $$, the possible rational zeros are simply the factors of the constant term: $$ \pm1, \pm2, \pm3, \pm4, \pm6, \pm9, \pm12, \pm18, \pm36 $$.

**Therefore, all possible rational zeros are:**

$$
\pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm 9, \pm 12, \pm 18, \pm 36
$$
All possible rational zeros are: $$ \pm1, \pm2, \pm3, \pm4, \pm6, \pm9, \pm12, \pm18, \pm36 $$.

Use the Rational Zero Theorem to list all possible rational zeros of the given pol the \( \pm \) symbol and separate your answers with a comma. For example : \( \pm 1, \pm 2 \) \( p(x)=x^{5}+17 x^{4}+7 x^{3}-12 x^{2}+x+36 \)

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