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The expression given is \( P(x) = (x - 2)^3 \).

To find the rational roots of this polynomial, we need to solve the equation \( P(x) = 0 \).

### Step-by-Step Solution:

1. **Set the polynomial equal to zero**:
   \[
   (x - 2)^3 = 0
   \]

2. **Solve for \( x \)**:
   - Take the cube root of both sides:
     \[
     x - 2 = 0
     \]
   - Solve for \( x \):
     \[
     x = 2
     \]

### Conclusion:
The only rational root of \( P(x) = (x - 2)^3 \) is \( x = 2 \).

Would you like further details or have any questions?

Here are five related questions you might consider:
1. How would the roots change if the equation were \( (x - 3)^3 = 0 \)?
2. What is the multiplicity of the root \( x = 2 \) in this polynomial?
3. How would you find the roots if the polynomial were \( P(x) = (x^2 - 4)^3 \)?
4. What happens to the graph of \( P(x) = (x - 2)^3 \) near the root \( x = 2 \)?
5. How would you verify if a root is rational?

**Tip:** When dealing with polynomial equations, the Rational Root Theorem can be a helpful tool to quickly determine possible rational roots.

Learn how to find the rational roots of the polynomial (x - 2)^3 with a detailed step-by-step solution. This problem involves polynomial roots and applications of the cube root formula. Suitable for students in Grades 9-12.

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