Factor polynomial $$ 6x^{2}+72x-78 $$

$$ 6x^{2}+72x-78 = 6( x-1 )( x+13 ) $$

Step 1 :

After factoring out $ 6 $ we have:

$$ 6x^{2}+72x-78 = 6 ( x^{2}+12x-13 ) $$

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:

$$ \color{blue}{ b = 12 } ~ \text{ and } ~ \color{red}{ c = -13 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ 12 } $ and multiply to $ \color{red}{ -13 } $.

Step 3: Find out pairs of numbers with a product of $\color{red}{ c = -13 }$.

PRODUCT = -13
-1     13	1     -13

Step 4: Find out which pair sums up to $\color{blue}{ b = 12 }$

PRODUCT = -13 and SUM = 12
-1     13	1     -13

Step 5: Put -1 and 13 into placeholders to get factored form.

$$ \begin{aligned} x^{2}+12x-13 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ x^{2}+12x-13 & = (x -1)(x + 13) \end{aligned} $$

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