Factor polynomial $$ x^{2}-23x-50 $$

$$ x^{2}-23x-50 = ( x+2 )( x-25 ) $$

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:

$$ \color{blue}{ b = -23 } ~ \text{ and } ~ \color{red}{ c = -50 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ -23 } $ and multiply to $ \color{red}{ -50 } $.

Step 2: Find out pairs of numbers with a product of $\color{red}{ c = -50 }$.

PRODUCT = -50
-1     50	1     -50
-2     25	2     -25
-5     10	5     -10

Step 3: Find out which pair sums up to $\color{blue}{ b = -23 }$

PRODUCT = -50 and SUM = -23
-1     50	1     -50
-2     25	2     -25
-5     10	5     -10

Step 4: Put 2 and -25 into placeholders to get factored form.

$$ \begin{aligned} x^{2}-23x-50 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ x^{2}-23x-50 & = (x + 2)(x -25) \end{aligned} $$

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