Factor polynomial $$ -6x^{2}-24x-40 $$

$$ -6x^{2}-24x-40 = ( -2 )( 3x^{2}+12x+20 ) $$

Step 1 :

After factoring out $ -2 $ we have:

$$ -6x^{2}-24x-40 = -2 ( 3x^{2}+12x+20 ) $$

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:

$$ a = 3 , b = 12 ~ \text{ and } ~ c = 20 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 3 }$ by the constant term $\color{blue}{c = 20} $.

$$ a \cdot c = 60 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = 60 $ and add to $ b = 12 $.

Step 5: All pairs of numbers with a product of $ 60 $ are:

PRODUCT = 60
1     60	-1     -60
2     30	-2     -30
3     20	-3     -20
4     15	-4     -15
5     12	-5     -12
6     10	-6     -10

Step 6: Find out which factor pair sums up to $\color{blue}{ b = 12 }$

Step 7: Because none of these pairs will give us a sum of $ \color{blue}{ 12 }$, we conclude the polynomial cannot be factored.

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