Step 1 :

After factoring out $ 6s $ we have:

$$ 12s^{3}-18s^{2}+48s = 6s ( 2s^{2}-3s+8 ) $$

Step 2 :

Step 2: 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:

$$ a = 2 , b = -3 ~ \text{ and } ~ c = 8 $$

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

$$ a \cdot c = 16 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = 16 $ and add to $ b = -3 $.

Step 5: All pairs of numbers with a product of $ 16 $ are:

PRODUCT = 16
1     16	-1     -16
2     8	-2     -8
4     4	-4     -4

Step 6: Find out which factor pair sums up to $\color{blue}{ b = -3 }$

Step 7: Because none of these pairs will give us a sum of $ \color{blue}{ -3 }$, we conclude the polynomial cannot be factored.

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