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:

$$ \color{blue}{ b = -4 } ~ \text{ and } ~ \color{red}{ c = -32 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ -4 } $ and multiply to $ \color{red}{ -32 } $.

Step 2: Find out pairs of numbers with a product of $\color{red}{ c = -32 }$.

PRODUCT = -32
-1     32	1     -32
-2     16	2     -16
-4     8	4     -8

Step 3: Find out which pair sums up to $\color{blue}{ b = -4 }$

PRODUCT = -32 and SUM = -4
-1     32	1     -32
-2     16	2     -16
-4     8	4     -8

Step 4: Put 4 and -8 into placeholders to get factored form.

$$ \begin{aligned} b^{2}-4b-32 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ b^{2}-4b-32 & = (x + 4)(x -8) \end{aligned} $$

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