Step 1: Identify constants $ \color{blue}{ b }$ and $\color{red}{ c }$. ( $ \color{blue}{ b }$ is a number in front of the $ x $ term and $ \color{red}{ c } $ is a constant). In our case:

$$ \color{blue}{ b = 2 } ~ \text{ and } ~ \color{red}{ c = -24 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ 2 } $ and multiply to $ \color{red}{ -24 } $.

Step 2: Find out pairs of numbers with a product of $\color{red}{ c = -24 }$.

PRODUCT = -24
-1     24	1     -24
-2     12	2     -12
-3     8	3     -8
-4     6	4     -6

Step 3: Find out which pair sums up to $\color{blue}{ b = 2 }$

PRODUCT = -24 and SUM = 2
-1     24	1     -24
-2     12	2     -12
-3     8	3     -8
-4     6	4     -6

Step 4: Put -4 and 6 into placeholders to get factored form.

$$ \begin{aligned} k^{2}+2k-24 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ k^{2}+2k-24 & = (x -4)(x + 6) \end{aligned} $$

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