To solve the expression \( x^2 - 4x - 12 \), let's look at how to factor it.

1. The expression \( x^2 - 4x - 12 \) is a quadratic equation of the form \( ax^2 + bx + c \), where \( a = 1 \), \( b = -4 \), and \( c = -12 \).
2. To factor it, we need two numbers that multiply to \( c = -12 \) and add up to \( b = -4 \).
3. The numbers that satisfy these conditions are \( -6 \) and \( +2 \) because:
   - \( -6 \times 2 = -12 \)
   - \( -6 + 2 = -4 \)

So, we can write the expression as:
\[
x^2 - 4x - 12 = (x - 6)(x + 2)
\]

### Answer:
The factored form of \( x^2 - 4x - 12 \) is:
\[
(x - 6)(x + 2)
\]

Would you like a deeper explanation or have any questions?

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Here are some related questions that might interest you:
1. How would you solve the equation if it were set to zero, \( x^2 - 4x - 12 = 0 \)?
2. What is the vertex form of the quadratic equation \( x^2 - 4x - 12 \)?
3. How can we determine the roots of any quadratic equation using the quadratic formula?
4. What is the graphical interpretation of factoring a quadratic equation?
5. How do we complete the square for the expression \( x^2 - 4x - 12 \)?

**Tip:** For any quadratic expression, factoring, completing the square, or using the quadratic formula are all methods to find roots and rewrite the expression.

Understand how to factor the quadratic equation x^2 - 4x - 12 through a detailed solution. Learn about factoring techniques, identifying numbers that multiply to -12 and add to -4, and rewriting the expression as (x - 6)(x + 2). Ideal for students in Grades 8-10.

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