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The expression given is:

\[
x^2 - 3x - 18
\]

We need to factor this quadratic expression.

### Step 1: Identify coefficients
The quadratic expression is in the form \( ax^2 + bx + c \), where:
- \( a = 1 \)
- \( b = -3 \)
- \( c = -18 \)

### Step 2: Find two numbers that multiply to \( a \times c = 1 \times -18 = -18 \) and add to \( b = -3 \).

The pair of numbers that satisfy these conditions are \( 3 \) and \( -6 \), because:
- \( 3 \times (-6) = -18 \)
- \( 3 + (-6) = -3 \)

### Step 3: Rewrite the middle term
Now, rewrite the quadratic as:
\[
x^2 + 3x - 6x - 18
\]

### Step 4: Factor by grouping
Group the terms as:
\[
(x^2 + 3x) - (6x + 18)
\]
Now, factor out the greatest common factor (GCF) from each group:
\[
x(x + 3) - 6(x + 3)
\]

### Step 5: Factor out the common binomial
\[
(x - 6)(x + 3)
\]

### Final Answer:
The factorization of \( x^2 - 3x - 18 \) is:
\[
(x - 6)(x + 3)
\]

Would you like more details on any step?

Here are 5 related questions:
1. How do you solve a quadratic equation by factoring?
2. What is the difference between factoring and expanding quadratic expressions?
3. Can all quadratic expressions be factored easily?
4. How do you apply the quadratic formula if factoring doesn't work?
5. What is the significance of the discriminant in quadratic equations?

**Tip**: When factoring, always check if there's a common factor across all terms before applying more advanced methods.

This page explains how to factor the quadratic expression x^2 - 3x - 18 step by step. It covers essential algebra concepts like factoring by grouping and identifying coefficients. Suitable for students in Grades 7-9.

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