Factor polynomial $$ 6k^{3}-12k^{2}+9k $$

$$ 6k^{3}-12k^{2}+9k = 3k( 2k^{2}-4k+3 ) $$

Step 1 :

After factoring out $ 3k $ we have:

$$ 6k^{3}-12k^{2}+9k = 3k ( 2k^{2}-4k+3 ) $$

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:

$$ a = 2 , b = -4 ~ \text{ and } ~ c = 3 $$

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

$$ a \cdot c = 6 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = 6 $ and add to $ b = -4 $.

Step 5: All pairs of numbers with a product of $ 6 $ are:

PRODUCT = 6
1     6	-1     -6
2     3	-2     -3

Step 6: Find out which factor pair sums up to $\color{blue}{ b = -4 }$

Step 7: Because none of these pairs will give us a sum of $ \color{blue}{ -4 }$, we conclude the polynomial cannot be factored.

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