To factorize the quadratic expression \(x^2 - 3x - 2\), we can follow these steps:

1. **Identify the coefficients:**
   - The coefficient of \(x^2\) is \(1\).
   - The coefficient of \(x\) is \(-3\).
   - The constant term is \(-2\).

2. **Find two numbers that multiply to** the constant term \(-2\) and add up to the coefficient of \(x\) \(-3\). These numbers are \(-2\) and \(-1\) because:
   \[
   (-2) \times 1 = -2
   \]
   \[
   -2 + (-1) = -3
   \]

3. **Rewrite the middle term** using these two numbers:
   \[
   x^2 - 2x - x - 2
   \]

4. **Factor by grouping:**
   \[
   (x^2 - 2x) - (x + 2)
   \]
   Factor out the common factors from each group:
   \[
   x(x - 2) - 1(x - 2)
   \]

5. **Factor out the common binomial factor:**
   \[
   (x - 2)(x + 1)
   \]

So, the factorized form of the expression \(x^2 - 3x - 2\) is \(\boxed{(x - 2)(x + 1)}\).

Would you like more details or have any questions?

Here are five related questions for further practice:
1. Factorize \(x^2 + 5x + 6\).
2. Factorize \(x^2 - 7x + 10\).
3. Solve the equation \(x^2 - 4x - 12 = 0\) by factoring.
4. Factorize \(x^2 + 2x - 8\).
5. Factorize \(x^2 - 6x + 9\).

**Tip:** When the coefficient of \(x^2\) is \(1\), look for two numbers that multiply to the constant term and add up to the coefficient of \(x\). This makes factorization simpler.

Learn how to factorize the quadratic expression x^2 - 3x - 2 with a detailed step-by-step solution. This problem covers key algebraic concepts, including factorization of quadratic equations. Suitable for students in Grades 9-12.

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