Step 1 :

After factoring out $ 5 $ we have:

$$ 5x^{2}-40x-50 = 5 ( x^{2}-8x-10 ) $$

Step 2 :

Step 2: 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:

$$ \color{blue}{ b = -8 } ~ \text{ and } ~ \color{red}{ c = -10 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ -8 } $ and multiply to $ \color{red}{ -10 } $.

Step 3: Find out pairs of numbers with a product of $\color{red}{ c = -10 }$.

PRODUCT = -10
-1     10	1     -10
-2     5	2     -5

Step 4: Because none of these pairs will give us a sum of $ \color{blue}{ -8 }$, we conclude the polynomial cannot be factored.

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