To solve the quadratic equation \( x^2 - 3x + 2 = 0 \), we will use factorization.

### Step-by-step solution:

1. **Write the equation**:  
   \[
   x^2 - 3x + 2 = 0
   \]

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

   These numbers are \( -1 \) and \( -2 \), since:
   \[
   (-1) \times (-2) = 2 \quad \text{and} \quad (-1) + (-2) = -3
   \]

3. **Write the factors**:  
   \[
   (x - 1)(x - 2) = 0
   \]

4. **Set each factor to zero**:  
   \[
   x - 1 = 0 \quad \text{or} \quad x - 2 = 0
   \]

5. **Solve for \( x \)**:  
   \[
   x = 1 \quad \text{or} \quad x = 2
   \]

### Final Answer:  
The solutions to the equation \( x^2 - 3x + 2 = 0 \) are \( x = 1 \) and \( x = 2 \).

Would you like a detailed explanation of any step?

Here are 5 related questions to expand your understanding:
1. How can we use the quadratic formula to solve \( x^2 - 3x + 2 = 0 \)?
2. What are other methods for solving quadratic equations besides factoring?
3. How do you know when a quadratic equation can be factored easily?
4. What is the meaning of the discriminant in quadratic equations?
5. Can you always factor a quadratic equation?

**Tip**: Always check your factorization by expanding the factors back to ensure they match the original quadratic equation.

Learn how to solve the quadratic equation x^2 - 3x + 2 = 0 using factorization. This step-by-step guide explains how to factor the quadratic, identify the roots, and apply key algebraic concepts. Perfect for students in Grades 7-9.

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