Factor polynomial $$ x^{2}-12x-364 $$

$$ x^{2}-12x-364 = ( x+14 )( x-26 ) $$

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:

$$ \color{blue}{ b = -12 } ~ \text{ and } ~ \color{red}{ c = -364 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ -12 } $ and multiply to $ \color{red}{ -364 } $.

Step 2: Find out pairs of numbers with a product of $\color{red}{ c = -364 }$.

PRODUCT = -364
-1     364	1     -364
-2     182	2     -182
-4     91	4     -91
-7     52	7     -52
-13     28	13     -28
-14     26	14     -26

Step 3: Find out which pair sums up to $\color{blue}{ b = -12 }$

PRODUCT = -364 and SUM = -12
-1     364	1     -364
-2     182	2     -182
-4     91	4     -91
-7     52	7     -52
-13     28	13     -28
-14     26	14     -26

Step 4: Put 14 and -26 into placeholders to get factored form.

$$ \begin{aligned} x^{2}-12x-364 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ x^{2}-12x-364 & = (x + 14)(x -26) \end{aligned} $$

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