Factor polynomial $$ x^{2}-4x-5 $$

$$ x^{2}-4x-5 = ( x+1 )( x-5 ) $$

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:

$$ \color{blue}{ b = -4 } ~ \text{ and } ~ \color{red}{ c = -5 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ -4 } $ and multiply to $ \color{red}{ -5 } $.

Step 2: Find out pairs of numbers with a product of $\color{red}{ c = -5 }$.

PRODUCT = -5
-1     5	1     -5

Step 3: Find out which pair sums up to $\color{blue}{ b = -4 }$

PRODUCT = -5 and SUM = -4
-1     5	1     -5

Step 4: Put 1 and -5 into placeholders to get factored form.

$$ \begin{aligned} x^{2}-4x-5 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ x^{2}-4x-5 & = (x + 1)(x -5) \end{aligned} $$

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