Factorizing a cubic polynomial can be approached in several ways, depending on the structure of the polynomial. Here's a general method you can follow:

### Steps to Factorize a Cubic Polynomial:

1. **Identify the Polynomial**: Let's say you have a cubic polynomial of the form:
   \[
   P(x) = ax^3 + bx^2 + cx + d
   \]

2. **Look for Rational Roots Using the Rational Root Theorem**:
   - The Rational Root Theorem suggests that any rational root of the polynomial is a factor of the constant term \( d \) divided by a factor of the leading coefficient \( a \).
   - List all possible rational roots: \( \pm \frac{\text{factors of } d}{\text{factors of } a} \).

3. **Test Possible Roots**:
   - Substitute these possible rational roots into the polynomial \( P(x) \). If \( P(r) = 0 \) for some root \( r \), then \( x = r \) is a root of the polynomial.
   - When you find a root \( r \), \( x - r \) is a factor of the polynomial.

4. **Factor Out the Root**:
   - Once you identify a root \( r \), perform polynomial division or use synthetic division to divide \( P(x) \) by \( x

Learn how to factorize a cubic polynomial using the Rational Root Theorem and step-by-step methods. This guide covers identifying polynomial structure, testing rational roots, and factorizing using synthetic division or polynomial division. Suitable for high school students and beyond.

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