Step 1: Identify constants $ a $ , $ b $ and $ c $.
$ a $ is a number in front of the $ x^2 $ term $ b $ is a number in front of the $ x $ term and $ c $ is a constant. In this case:

$$ a = 3 , b = -26 ~ \text{ and } ~ c = -9 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 3 }$ by the constant term $\color{blue}{c = -9} $.

$$ a \cdot c = -27 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = -27 $ and add to $ b = -26 $.

Step 4: All pairs of numbers with a product of $ -27 $ are:

PRODUCT = -27
-1     27	1     -27
-3     9	3     -9

Step 5: Find out which factor pair sums up to $\color{blue}{ b = -26 }$

PRODUCT = -27 and SUM = -26
-1     27	1     -27
-3     9	3     -9

Step 6: Replace middle term $ -26 x $ with $ x-27x $:

$$ 3x^{2}-26x-9 = 3x^{2}+x-27x-9 $$

Step 7: Apply factoring by grouping. Factor $ x $ out of the first two terms and $ -9 $ out of the last two terms.

$$ 3x^{2}+x-27x-9 = x\left(3x+1\right) -9\left(3x+1\right) = \left(x-9\right) \left(3x+1\right) $$

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