Step 1 :

After factoring out $ 4 $ we have:

$$ 16x^{2}+100x-136 = 4 ( 4x^{2}+25x-34 ) $$

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:

$$ a = 4 , b = 25 ~ \text{ and } ~ c = -34 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 4 }$ by the constant term $\color{blue}{c = -34} $.

$$ a \cdot c = -136 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = -136 $ and add to $ b = 25 $.

Step 5: All pairs of numbers with a product of $ -136 $ are:

PRODUCT = -136
-1     136	1     -136
-2     68	2     -68
-4     34	4     -34
-8     17	8     -17

Step 6: Find out which factor pair sums up to $\color{blue}{ b = 25 }$

Step 7: Because none of these pairs will give us a sum of $ \color{blue}{ 25 }$, we conclude the polynomial cannot be factored.

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