Question

factor. $x^{2}+4x-12$

Explanation:

Step1: Find pair of factors for -12

We need two numbers that multiply to $-12$ and add to $4$. These numbers are $6$ and $-2$, since $6 \times (-2) = -12$ and $6 + (-2) = 4$.

Step2: Split middle term and factor

Rewrite the quadratic using the pair, then factor by grouping:

$$\begin{align*} x^2 + 4x - 12 &= x^2 + 6x - 2x - 12 \\ &= x(x + 6) - 2(x + 6) \\ &= (x + 6)(x - 2) \end{align*}$$

Answer:

$(x + 6)(x - 2)$