Factor polynomial $$ -18x^{3}-12x^{2}-6x $$

$$ -18x^{3}-12x^{2}-6x = ( -6 )x( 3x^{2}+2x+1 ) $$

Step 1 :

After factoring out $ -6x $ we have:

$$ -18x^{3}-12x^{2}-6x = -6x ( 3x^{2}+2x+1 ) $$

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:

$$ a = 3 , b = 2 ~ \text{ and } ~ c = 1 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 3 }$ by the constant term $\color{blue}{c = 1} $.

$$ a \cdot c = 3 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = 3 $ and add to $ b = 2 $.

Step 5: All pairs of numbers with a product of $ 3 $ are:

PRODUCT = 3
1     3	-1     -3

Step 6: Find out which factor pair sums up to $\color{blue}{ b = 2 }$

Step 7: Because none of these pairs will give us a sum of $ \color{blue}{ 2 }$, we conclude the polynomial cannot be factored.

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