Step 1 :

After factoring out $ 8 $ we have:

$$ 64x^{2}-16x+40 = 8 ( 8x^{2}-2x+5 ) $$

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:

$$ a = 8 , b = -2 ~ \text{ and } ~ c = 5 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 8 }$ by the constant term $\color{blue}{c = 5} $.

$$ a \cdot c = 40 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = 40 $ and add to $ b = -2 $.

Step 5: All pairs of numbers with a product of $ 40 $ are:

PRODUCT = 40
1     40	-1     -40
2     20	-2     -20
4     10	-4     -10
5     8	-5     -8

Step 6: Find out which factor pair sums up to $\color{blue}{ b = -2 }$

Step 7: Because none of these pairs will give us a sum of $ \color{blue}{ -2 }$, we conclude the polynomial cannot be factored.

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