Step 1 :

After factoring out $ -4 $ we have:

$$ -188p^{2}-288p+28 = -4 ( 47p^{2}+72p-7 ) $$

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:

$$ a = 47 , b = 72 ~ \text{ and } ~ c = -7 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 47 }$ by the constant term $\color{blue}{c = -7} $.

$$ a \cdot c = -329 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = -329 $ and add to $ b = 72 $.

Step 5: All pairs of numbers with a product of $ -329 $ are:

PRODUCT = -329
-1     329	1     -329
-7     47	7     -47

Step 6: Find out which factor pair sums up to $\color{blue}{ b = 72 }$

Step 7: Because none of these pairs will give us a sum of $ \color{blue}{ 72 }$, we conclude the polynomial cannot be factored.

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