The given equation is a quadratic equation:

\[
x^2 - 3x + 2 = 0
\]

To solve this, we can factor the quadratic expression.

### Step 1: Factor the quadratic expression

We look for two numbers that multiply to \(2\) (the constant term) and add up to \(-3\) (the coefficient of \(x\)).

These numbers are \(-1\) and \(-2\), because:

\[
-1 \times -2 = 2 \quad \text{and} \quad -1 + (-2) = -3
\]

So, we can rewrite the quadratic equation as:

\[
(x - 1)(x - 2) = 0
\]

### Step 2: Solve for \(x\)

Now, we set each factor equal to zero:

\[
x - 1 = 0 \quad \text{or} \quad x - 2 = 0
\]

Solving these gives:

\[
x = 1 \quad \text{or} \quad x = 2
\]

### Solution:

The solutions to the equation are:

\[
x = 1 \quad \text{or} \quad x = 2
\]

Would you like more details or have any questions?

Here are some related questions for practice:
1. Solve the equation \(x^2 - 5x + 6 = 0\).
2. Factor and solve \(x^2 + 4x + 3 = 0\).
3. Use the quadratic formula to solve \(x^2 - 3x + 2 = 0\).
4. Solve \(x^2 - 4x + 4 = 0\) by factoring.
5. Solve the equation \(x^2 + 2x - 8 = 0\).

**Tip:** Always check if a quadratic equation can be factored easily before using more advanced methods like the quadratic formula.

Explore how to solve the quadratic equation x^2 - 3x + 2 using factoring methods. This step-by-step guide walks through algebraic concepts, such as factoring quadratic expressions and using the Zero Product Property. Ideal for students in Grades 8-10.

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