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:

$$ \color{blue}{ b = -48 } ~ \text{ and } ~ \color{red}{ c = -324 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ -48 } $ and multiply to $ \color{red}{ -324 } $.

Step 2: Find out pairs of numbers with a product of $\color{red}{ c = -324 }$.

PRODUCT = -324
-1     324	1     -324
-2     162	2     -162
-3     108	3     -108
-4     81	4     -81
-6     54	6     -54
-9     36	9     -36
-12     27	12     -27
-18     18	18     -18

Step 3: Find out which pair sums up to $\color{blue}{ b = -48 }$

PRODUCT = -324 and SUM = -48
-1     324	1     -324
-2     162	2     -162
-3     108	3     -108
-4     81	4     -81
-6     54	6     -54
-9     36	9     -36
-12     27	12     -27
-18     18	18     -18

Step 4: Put 6 and -54 into placeholders to get factored form.

$$ \begin{aligned} x^{2}-48x-324 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ x^{2}-48x-324 & = (x + 6)(x -54) \end{aligned} $$

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