Factor the trinomial.

*x*2 + 4*x* − 12

To factor the trinomial \(x^2 + 4x - 12\), we need to find two numbers that multiply to \(-12\) (the constant term) and add to \(4\) (the coefficient of the middle term). 

Let's follow the steps:

1. **Identify the coefficients**: 
   - \(a = 1\) (coefficient of \(x^2\))
   - \(b = 4\) (coefficient of \(x\))
   - \(c = -12\) (constant term)

2. **Find two numbers that multiply to \(a \times c = -12\) and add to \(b = 4\)**:
   - The numbers that work are \(6\) and \(-2\) because:
     - \(6 \times -2 = -12\)
     - \(6 + (-2) = 4\)

3. **Rewrite the middle term using these two numbers**:
   \[
   x^2 + 6x - 2x - 12
   \]

4. **Factor by grouping**:
   \[
   x(x + 6) - 2(x + 6)
   \]

5. **Factor out the common binomial**:
   \[
   (x - 2)(x + 6)
   \]

So, the factored form of the trinomial \(x^2 + 4x - 12\) is \(\boxed{(x - 2)(x + 6)}\).

Would you like more details, or do you have any questions?

### Related Questions:
1. How do you factor trinomials when the leading coefficient is not 1?
2. What is the difference between factoring by grouping and using the quadratic formula?
3. Can all quadratic trinomials be factored using integers?
4. How do you factor perfect square trinomials?
5. What are the applications of factoring trinomials in real-world problems?

**Tip:** When factoring, always check your work by expanding the factors to ensure they multiply back to the original expression.

Learn how to factor the trinomial x^2 + 4x - 12 with a step-by-step solution. This problem covers key algebraic concepts, including factoring quadratic trinomials. Suitable for students in Grades 7-9.

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