Step 1: 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:

$$ a = 7 , b = 41 ~ \text{ and } ~ c = -56 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 7 }$ by the constant term $\color{blue}{c = -56} $.

$$ a \cdot c = -392 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = -392 $ and add to $ b = 41 $.

Step 4: All pairs of numbers with a product of $ -392 $ are:

PRODUCT = -392
-1     392	1     -392
-2     196	2     -196
-4     98	4     -98
-7     56	7     -56
-8     49	8     -49
-14     28	14     -28

Step 5: Find out which factor pair sums up to $\color{blue}{ b = 41 }$

PRODUCT = -392 and SUM = 41
-1     392	1     -392
-2     196	2     -196
-4     98	4     -98
-7     56	7     -56
-8     49	8     -49
-14     28	14     -28

Step 6: Replace middle term $ 41 x $ with $ 49x-8x $:

$$ 7x^{2}+41x-56 = 7x^{2}+49x-8x-56 $$

Step 7: Apply factoring by grouping. Factor $ 7x $ out of the first two terms and $ -8 $ out of the last two terms.

$$ 7x^{2}+49x-8x-56 = 7x\left(x+7\right) -8\left(x+7\right) = \left(7x-8\right) \left(x+7\right) $$

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