Question

factor completely.
$k^2 - 2k - 24$
options:
$(k + 4)(k - 6)$
$(k - 4)(k + 6)$
$(k + 6)(k - 1)$
$(k - 4)(k + 6)$ (note: the last option in the image might have a typo, but the main problem is to factor $k^2 - 2k - 24$ with these choices)

Explanation:

Step1: Identify $a,b,c$ for $ax^2+bx+c$

For $k^2-2k-24$, $a=1$, $b=-2$, $c=-24$

Step2: Find pair with product $ac$, sum $b$

Need two numbers: product $1\times(-24)=-24$, sum $-2$.
The numbers are $4$ and $-6$ (since $4\times(-6)=-24$, $4+(-6)=-2$)

Step3: Split middle term and factor

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

Answer:

A. $(k+4)(k-6)$