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:

$$ a = 3 , b = -28 ~ \text{ and } ~ c = 9 $$

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 = -28 $.

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 $\color{blue}{ b = -28 }$

PRODUCT = 27 and SUM = -28
1     27	-1     -27
3     9	-3     -9

Step 6: Replace middle term $ -28 x $ with $ -x-27x $:

$$ 3x^{2}-28x+9 = 3x^{2}-x-27x+9 $$

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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