Factor polynomial $$ x^{2}-5x-36 $$

$$ x^{2}-5x-36 = ( x+4 )( x-9 ) $$

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:

$$ \color{blue}{ b = -5 } ~ \text{ and } ~ \color{red}{ c = -36 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ -5 } $ and multiply to $ \color{red}{ -36 } $.

Step 2: Find out pairs of numbers with a product of $\color{red}{ c = -36 }$.

PRODUCT = -36
-1     36	1     -36
-2     18	2     -18
-3     12	3     -12
-4     9	4     -9
-6     6	6     -6

Step 3: Find out which pair sums up to $\color{blue}{ b = -5 }$

PRODUCT = -36 and SUM = -5
-1     36	1     -36
-2     18	2     -18
-3     12	3     -12
-4     9	4     -9
-6     6	6     -6

Step 4: Put 4 and -9 into placeholders to get factored form.

$$ \begin{aligned} x^{2}-5x-36 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ x^{2}-5x-36 & = (x + 4)(x -9) \end{aligned} $$

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