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:
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.