Factor polynomial $$ v^{2}+4v-12 $$

$$ v^{2}+4v-12 = ( v-2 )( v+6 ) $$

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:

$$ \color{blue}{ b = 4 } ~ \text{ and } ~ \color{red}{ c = -12 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ 4 } $ and multiply to $ \color{red}{ -12 } $.

Step 2: 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 3: Find out which pair sums up to $\color{blue}{ b = 4 }$

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

Step 4: Put -2 and 6 into placeholders to get factored form.

$$ \begin{aligned} v^{2}+4v-12 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ v^{2}+4v-12 & = (x -2)(x + 6) \end{aligned} $$

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