To factor the quadratic expression \( x^2 + 3x - 2 \), we need to find two numbers that multiply to give \( -2 \) (the constant term) and add to give \( 3 \) (the coefficient of the middle term).

Let's go step by step:

### Step 1: Identify the terms.
- Coefficient of \( x^2 \): \( 1 \)
- Coefficient of \( x \): \( 3 \)
- Constant term: \( -2 \)

### Step 2: Find two numbers.
We are looking for two numbers that multiply to \( -2 \) and add to \( 3 \).

These numbers are \( 2 \) and \( -1 \), because:
- \( 2 \times (-1) = -2 \)
- \( 2 + (-1) = 3 \)

### Step 3: Write the factored form.
Using these numbers, we can rewrite the expression as:

\[
x^2 + 3x - 2 = (x + 2)(x - 1)
\]

So, the factored form of \( x^2 + 3x - 2 \) is:

\[
(x + 2)(x - 1)
\]

Would you like further details or have any questions?

Here are some related questions:
1. How do you factor quadratic equations where the leading coefficient is greater than 1?
2. What is the difference between factoring and expanding quadratic expressions?
3. How can you verify if your factored form is correct?
4. How does the quadratic formula relate to factoring?
5. How would you solve the equation \( x^2 + 3x - 2 = 0 \) using the factored form?

**Tip:** Always check your factored expression by expanding it back to ensure you get the original quadratic equation.

Learn how to factor the quadratic expression x^2 + 3x - 2 with a clear, step-by-step solution. This problem covers key algebraic concepts, including factoring methods and working with quadratic expressions. Suitable for students in Grades 8-10.

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