Question

13/22
factor $k^2 - 2k - 24$
$(k-4)(k+6)$
$(k+4)(k+6)$
$(k+6)(k-1)$
$(k+4)(k-6)$
youre immune to an incorrect answer.

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 $-6$.

Step3: Split middle term and factor

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

Step4: Verify by expanding factors

$$(k+4)(k-6)=k^2-6k+4k-24=k^2-2k-24$$

Answer:

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