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:

$$ a = 8 , b = -7 ~ \text{ and } ~ c = -100 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 8 }$ by the constant term $\color{blue}{c = -100} $.

$$ a \cdot c = -800 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = -800 $ and add to $ b = -7 $.

Step 4: All pairs of numbers with a product of $ -800 $ are:

PRODUCT = -800
-1     800	1     -800
-2     400	2     -400
-4     200	4     -200
-5     160	5     -160
-8     100	8     -100
-10     80	10     -80
-16     50	16     -50
-20     40	20     -40
-25     32	25     -32

Step 5: Find out which factor pair sums up to $\color{blue}{ b = -7 }$

PRODUCT = -800 and SUM = -7
-1     800	1     -800
-2     400	2     -400
-4     200	4     -200
-5     160	5     -160
-8     100	8     -100
-10     80	10     -80
-16     50	16     -50
-20     40	20     -40
-25     32	25     -32

Step 6: Replace middle term $ -7 x $ with $ 25x-32x $:

$$ 8x^{2}-7x-100 = 8x^{2}+25x-32x-100 $$

Step 7: Apply factoring by grouping. Factor $ x $ out of the first two terms and $ -4 $ out of the last two terms.

$$ 8x^{2}+25x-32x-100 = x\left(8x+25\right) -4\left(8x+25\right) = \left(x-4\right) \left(8x+25\right) $$

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