Step 1 :

After factoring out $ 3 $ we have:

$$ 3v^{2}+90v-93 = 3 ( v^{2}+30v-31 ) $$

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:

$$ \color{blue}{ b = 30 } ~ \text{ and } ~ \color{red}{ c = -31 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ 30 } $ and multiply to $ \color{red}{ -31 } $.

Step 3: Find out pairs of numbers with a product of $\color{red}{ c = -31 }$.

PRODUCT = -31
-1     31	1     -31

Step 4: Find out which pair sums up to $\color{blue}{ b = 30 }$

PRODUCT = -31 and SUM = 30
-1     31	1     -31

Step 5: Put -1 and 31 into placeholders to get factored form.

$$ \begin{aligned} v^{2}+30v-31 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ v^{2}+30v-31 & = (x -1)(x + 31) \end{aligned} $$

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