Factor polynomial $$ 5a^{2}-22a+8 $$

$$ 5a^{2}-22a+8 = ( a-4 )( 5a-2 ) $$

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:

$$ a = 5 , b = -22 ~ \text{ and } ~ c = 8 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 5 }$ by the constant term $\color{blue}{c = 8} $.

$$ a \cdot c = 40 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = 40 $ and add to $ b = -22 $.

Step 4: 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 5: Find out which factor pair sums up to $\color{blue}{ b = -22 }$

PRODUCT = 40 and SUM = -22
1     40	-1     -40
2     20	-2     -20
4     10	-4     -10
5     8	-5     -8

Step 6: Replace middle term $ -22 x $ with $ -2x-20x $:

$$ 5x^{2}-22x+8 = 5x^{2}-2x-20x+8 $$

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

$$ 5x^{2}-2x-20x+8 = x\left(5x-2\right) -4\left(5x-2\right) = \left(x-4\right) \left(5x-2\right) $$

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