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:

$$ \color{blue}{ b = -17 } ~ \text{ and } ~ \color{red}{ c = -38 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ -17 } $ and multiply to $ \color{red}{ -38 } $.

Step 2: Find out pairs of numbers with a product of $\color{red}{ c = -38 }$.

PRODUCT = -38
-1     38	1     -38
-2     19	2     -19

Step 3: Find out which pair sums up to $\color{blue}{ b = -17 }$

PRODUCT = -38 and SUM = -17
-1     38	1     -38
-2     19	2     -19

Step 4: Put 2 and -19 into placeholders to get factored form.

$$ \begin{aligned} m^{2}-17m-38 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ m^{2}-17m-38 & = (x + 2)(x -19) \end{aligned} $$

Polynomial Factoring Calculator