Step 1 :

After factoring out $ -2 $ we have:

$$ -16x^{2}-30x+300 = -2 ( 8x^{2}+15x-150 ) $$

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:

$$ a = 8 , b = 15 ~ \text{ and } ~ c = -150 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 8 }$ by the constant term $\color{blue}{c = -150} $.

$$ a \cdot c = -1200 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = -1200 $ and add to $ b = 15 $.

Step 5: All pairs of numbers with a product of $ -1200 $ are:

PRODUCT = -1200
-1     1200	1     -1200
-2     600	2     -600
-3     400	3     -400
-4     300	4     -300
-5     240	5     -240
-6     200	6     -200
-8     150	8     -150
-10     120	10     -120
-12     100	12     -100
-15     80	15     -80
-16     75	16     -75
-20     60	20     -60
-24     50	24     -50
-25     48	25     -48
-30     40	30     -40

Step 6: Find out which factor pair sums up to $\color{blue}{ b = 15 }$

Step 7: Because none of these pairs will give us a sum of $ \color{blue}{ 15 }$, we conclude the polynomial cannot be factored.

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