Factor polynomial $$ x^{3}-5x^{2}-x $$

$$ x^{3}-5x^{2}-x = x( x^{2}-5x-1 ) $$

Step 1 :

After factoring out $ x $ we have:

$$ x^{3}-5x^{2}-x = x ( x^{2}-5x-1 ) $$

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:

$$ \color{blue}{ b = -5 } ~ \text{ and } ~ \color{red}{ c = -1 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ -5 } $ and multiply to $ \color{red}{ -1 } $.

Step 3: Find out pairs of numbers with a product of $\color{red}{ c = -1 }$.

PRODUCT = -1
-1     1	1     -1

Step 4: Because none of these pairs will give us a sum of $ \color{blue}{ -5 }$, we conclude the polynomial cannot be factored.

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