Step 1 :

After factoring out $ x $ we have:

$$ x^{3}-10x^{2}+50x = x ( x^{2}-10x+50 ) $$

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:

$$ \color{blue}{ b = -10 } ~ \text{ and } ~ \color{red}{ c = 50 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ -10 } $ and multiply to $ \color{red}{ 50 } $.

Step 3: 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 4: Because none of these pairs will give us a sum of $ \color{blue}{ -10 }$, we conclude the polynomial cannot be factored.

Polynomial Factoring Calculator