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:

$$ a = 3 , b = -25 ~ \text{ and } ~ c = 8 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 3 }$ by the constant term $\color{blue}{c = 8} $.

$$ a \cdot c = 24 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = 24 $ and add to $ b = -25 $.

Step 4: All pairs of numbers with a product of $ 24 $ are:

PRODUCT = 24
1     24	-1     -24
2     12	-2     -12
3     8	-3     -8
4     6	-4     -6

Step 5: Find out which factor pair sums up to $\color{blue}{ b = -25 }$

PRODUCT = 24 and SUM = -25
1     24	-1     -24
2     12	-2     -12
3     8	-3     -8
4     6	-4     -6

Step 6: Replace middle term $ -25 x $ with $ -x-24x $:

$$ 3x^{2}-25x+8 = 3x^{2}-x-24x+8 $$

Step 7: Apply factoring by grouping. Factor $ x $ out of the first two terms and $ -8 $ out of the last two terms.

$$ 3x^{2}-x-24x+8 = x\left(3x-1\right) -8\left(3x-1\right) = \left(x-8\right) \left(3x-1\right) $$

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