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The problem is asking to find one factor of the polynomial \( x^3 - 13x - 12 \).

### Steps to solve:
1. **Identify possible rational roots**: 
   By the Rational Root Theorem, the possible rational roots of the polynomial \( x^3 - 13x - 12 \) are factors of the constant term (-12) divided by factors of the leading coefficient (1). This gives the possible roots:
   \[
   \pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm 12
   \]

2. **Test these values in the polynomial** using substitution.

   - For \( x = 1 \):
     \[
     1^3 - 13(1) - 12 = 1 - 13 - 12 = -24 \quad (\text{Not a root})
     \]
   - For \( x = -1 \):
     \[
     (-1)^3 - 13(-1) - 12 = -1 + 13 - 12 = 0 \quad (\text{This is a root!})
     \]

Thus, \( x = -1 \) is a root.

3. **Factor the polynomial**:
   Since \( x = -1 \) is a root, we can use synthetic division to factor \( x^3 - 13x - 12 \) by \( x + 1 \).

   Performing synthetic division of \( x^3 - 13x - 12 \) by \( x + 1 \):

   \[
   \begin{array}{r|rrr}
   -1 & 1 & 0 & -13 & -12 \\
      &   & -1 & 1 & -12 \\
   \hline
      & 1 & -1 & -12 & 0 \\
   \end{array}
   \]

   The quotient is \( x^2 - x - 12 \).

4. **Factor the quadratic**:
   Now factor \( x^2 - x - 12 \):
   \[
   x^2 - x - 12 = (x - 4)(x + 3)
   \]

5. **Final factorization**:
   So, the complete factorization of \( x^3 - 13x - 12 \) is:
   \[
   (x + 1)(x - 4)(x + 3)
   \]

Thus, **one factor** of the polynomial is \( x + 1 \).

Would you like further details or explanations?

### Related Questions:
1. What is the Rational Root Theorem, and how is it applied to find roots?
2. Can synthetic division always be used to factor cubic polynomials?
3. How can we verify that a factorization is correct for any polynomial?
4. What is the process for factoring quadratic equations like \( x^2 - x - 12 \)?
5. How would this factorization change if the cubic polynomial had complex roots?

### Tip:
To factor polynomials easily, always start by testing small integer roots using the Rational Root Theorem.

Salah satu faktor dari polinomial x^3 - 13x - 12 adalah ...

Learn how to find a factor of the polynomial x^3 - 13x - 12 using the Rational Root Theorem and synthetic division. This step-by-step solution explains the process, including testing potential roots and factorizing the resulting quadratic equation. Suitable for students in Grades 10-12.

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