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:

$$ \color{blue}{ b = 16 } ~ \text{ and } ~ \color{red}{ c = -105 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ 16 } $ and multiply to $ \color{red}{ -105 } $.

Step 2: Find out pairs of numbers with a product of $\color{red}{ c = -105 }$.

PRODUCT = -105
-1     105	1     -105
-3     35	3     -35
-5     21	5     -21
-7     15	7     -15

Step 3: Find out which pair sums up to $\color{blue}{ b = 16 }$

PRODUCT = -105 and SUM = 16
-1     105	1     -105
-3     35	3     -35
-5     21	5     -21
-7     15	7     -15

Step 4: Put -5 and 21 into placeholders to get factored form.

$$ \begin{aligned} x^{2}+16x-105 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ x^{2}+16x-105 & = (x -5)(x + 21) \end{aligned} $$

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