Yes, the expression \( 3x^2 - 6x - 9 \) is factorable. To factor it, follow these steps:

1. **Find the Greatest Common Factor (GCF)**:
   The GCF of \( 3x^2, -6x, \) and \( -9 \) is 3. So, we factor out 3:
   \[
   3x^2 - 6x - 9 = 3(x^2 - 2x - 3)
   \]

2. **Factor the quadratic** \( x^2 - 2x - 3 \):
   We need to find two numbers that multiply to \(-3\) (the constant term) and add to \(-2\) (the coefficient of \(x\)). These numbers are \(-3\) and \(1\).

   So, we can rewrite \(x^2 - 2x - 3\) as:
   \[
   x^2 - 3x + x - 3
   \]

3. **Group the terms**:
   \[
   (x^2 - 3x) + (x - 3)
   \]

   Factor out the common terms in each group:
   \[
   x(x - 3) + 1(x - 3)
   \]

4. **Factor out the common binomial**:
   \[
   (x + 1)(x - 3)
   \]

5. **Write the fully factored form**:
   \[
   3(x + 1)(x - 3)
   \]

Therefore, \( 3x^2 - 6x - 9 = 3(x + 1)(x - 3) \).

Would you like more details or have any questions?

Here are some related questions to explore:

1. How do you find the GCF of a polynomial?
2. What are other methods for factoring quadratics?
3. Can all quadratic expressions be factored?
4. How do you verify if a factored expression is correct?
5. How does factoring help in solving equations?

**Tip:** Always start by looking for a GCF when factoring a polynomial; it simplifies the process significantly.

Learn how to factor the quadratic equation 3x^2 - 6x - 9 with a detailed step-by-step solution. This problem covers key algebraic concepts, including finding the Greatest Common Factor (GCF) and factoring by grouping. Suitable for students in Grades 9-10.

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