Factor polynomial $$ -16x^{2}-4x+382 $$

$$ -16x^{2}-4x+382 = ( -2 )( 8x^{2}+2x-191 ) $$

Step 1 :

After factoring out $ -2 $ we have:

$$ -16x^{2}-4x+382 = -2 ( 8x^{2}+2x-191 ) $$

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:

$$ a = 8 , b = 2 ~ \text{ and } ~ c = -191 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 8 }$ by the constant term $\color{blue}{c = -191} $.

$$ a \cdot c = -1528 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = -1528 $ and add to $ b = 2 $.

Step 5: All pairs of numbers with a product of $ -1528 $ are:

PRODUCT = -1528
-1     1528	1     -1528
-2     764	2     -764
-4     382	4     -382
-8     191	8     -191

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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