To solve the quadratic equation \( x^2 - 3x + 2 = 0 \), we can factor it.

1. First, we look for two numbers that multiply to \( 2 \) (the constant term) and add to \( -3 \) (the coefficient of \( x \)).
   - These numbers are \( -1 \) and \( -2 \), since \( (-1) \times (-2) = 2 \) and \( (-1) + (-2) = -3 \).

2. We can now factor the quadratic equation as:
   \[
   (x - 1)(x - 2) = 0
   \]

3. Using the zero-product property, set each factor equal to zero:
   \[
   x - 1 = 0 \quad \text{or} \quad x - 2 = 0
   \]

4. Solving for \( x \), we get:
   \[
   x = 1 \quad \text{or} \quad x = 2
   \]

Thus, the solutions to the equation are:
\[
x = 1 \quad \text{and} \quad x = 2
\]

Would you like more details on the factoring method or any other approach?

Here are some related questions to deepen your understanding:
1. How do you solve quadratic equations using the quadratic formula?
2. Can all quadratic equations be factored easily?
3. What is the discriminant, and how does it determine the number of solutions in a quadratic equation?
4. How would the solution change if the constant term was negative, such as \( x^2 - 3x - 2 = 0 \)?
5. Can you derive the vertex form of a quadratic equation from the standard form?

**Tip:** Always check your factorization by expanding the factored form to ensure it matches the original equation.

Learn how to solve the quadratic equation x^2 - 3x + 2 using factoring. This step-by-step guide demonstrates key algebraic concepts, including the zero-product property, and is suitable for students in Grades 7-9.

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