Factor polynomial $$ 6x^{2}-18x-72 $$

$$ 6x^{2}-18x-72 = 6( x^{2}-3x-12 ) $$

Step 1 :

After factoring out $ 6 $ we have:

$$ 6x^{2}-18x-72 = 6 ( x^{2}-3x-12 ) $$

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:

$$ \color{blue}{ b = -3 } ~ \text{ and } ~ \color{red}{ c = -12 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ -3 } $ and multiply to $ \color{red}{ -12 } $.

Step 3: Find out pairs of numbers with a product of $\color{red}{ c = -12 }$.

PRODUCT = -12
-1     12	1     -12
-2     6	2     -6
-3     4	3     -4

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

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