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:

$$ a = 2 , b = -15 ~ \text{ and } ~ c = -8 $$

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

$$ a \cdot c = -16 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = -16 $ and add to $ b = -15 $.

Step 4: All pairs of numbers with a product of $ -16 $ are:

PRODUCT = -16
-1     16	1     -16
-2     8	2     -8
-4     4	4     -4

Step 5: Find out which factor pair sums up to $\color{blue}{ b = -15 }$

PRODUCT = -16 and SUM = -15
-1     16	1     -16
-2     8	2     -8
-4     4	4     -4

Step 6: Replace middle term $ -15 x $ with $ x-16x $:

$$ 2x^{2}-15x-8 = 2x^{2}+x-16x-8 $$

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

$$ 2x^{2}+x-16x-8 = x\left(2x+1\right) -8\left(2x+1\right) = \left(x-8\right) \left(2x+1\right) $$

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