Question

factor completely.
$x^2 - 2x - 24$

Explanation:

Step1: Find pair summing to -2, product -24

We need two numbers: $4$ and $-6$ (since $4 + (-6) = -2$, $4 \times (-6) = -24$)

Step2: Split middle term and factor

Rewrite $-2x$ as $4x - 6x$, then factor by grouping:

$$\begin{align*} x^2 - 2x - 24 &= x^2 + 4x - 6x - 24\\ &= x(x + 4) - 6(x + 4)\\ &= (x + 4)(x - 6) \end{align*}$$

Answer:

$(x + 4)(x - 6)$