Factor polynomial $$ -16x^{2}+36x+8 $$

$$ -16x^{2}+36x+8 = ( -4 )( 4x^{2}-9x-2 ) $$

Step 1 :

After factoring out $ -4 $ we have:

$$ -16x^{2}+36x+8 = -4 ( 4x^{2}-9x-2 ) $$

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:

$$ a = 4 , b = -9 ~ \text{ and } ~ c = -2 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 4 }$ by the constant term $\color{blue}{c = -2} $.

$$ a \cdot c = -8 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = -8 $ and add to $ b = -9 $.

Step 5: All pairs of numbers with a product of $ -8 $ are:

PRODUCT = -8
-1     8	1     -8
-2     4	2     -4

Step 6: Find out which factor pair sums up to $\color{blue}{ b = -9 }$

Step 7: Because none of these pairs will give us a sum of $ \color{blue}{ -9 }$, we conclude the polynomial cannot be factored.

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