To factor the expression [tex]\( x^2 + 4x - 12 \)[/tex], follow these steps:
1. Identify the quadratic expression:
The given quadratic expression is [tex]\( x^2 + 4x - 12 \)[/tex].
2. Set up the factoring form:
We want to express [tex]\(x^2 + 4x - 12\)[/tex] as a product of two binomials: [tex]\((x - a)(x + b)\)[/tex].
3. Find two numbers that multiply to the constant term and add to the coefficient of the linear term:
We need two numbers that multiply to [tex]\(-12\)[/tex] (the constant term) and add up to [tex]\(4\)[/tex] (the coefficient of the [tex]\(x\)[/tex] term).
4. Determine the correct pair of factors:
The numbers that satisfy these conditions are [tex]\(6\)[/tex] and [tex]\(-2\)[/tex]. This is because:
[tex]\[
6 \times (-2) = -12 \quad \text{and} \quad 6 + (-2) = 4.
\][/tex]
5. Write the factored form:
Substitute the numbers into the binomials to get the factorized form:
[tex]\[
(x - 2)(x + 6).
\][/tex]
Therefore, the factored form of the expression [tex]\(x^2 + 4x - 12\)[/tex] is
[tex]\[
(x - 2)(x + 6).
\][/tex]
This is the correct answer.
