Step 1 :

After factoring out $ 7x $ we have:

$$ 70x^{3}-231x^{2}+140x = 7x ( 10x^{2}-33x+20 ) $$

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:

$$ a = 10 , b = -33 ~ \text{ and } ~ c = 20 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 10 }$ by the constant term $\color{blue}{c = 20} $.

$$ a \cdot c = 200 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = 200 $ and add to $ b = -33 $.

Step 5: All pairs of numbers with a product of $ 200 $ are:

PRODUCT = 200
1     200	-1     -200
2     100	-2     -100
4     50	-4     -50
5     40	-5     -40
8     25	-8     -25
10     20	-10     -20

Step 6: Find out which factor pair sums up to $\color{blue}{ b = -33 }$

PRODUCT = 200 and SUM = -33
1     200	-1     -200
2     100	-2     -100
4     50	-4     -50
5     40	-5     -40
8     25	-8     -25
10     20	-10     -20

Step 7: Replace middle term $ -33 x $ with $ -8x-25x $:

$$ 10x^{2}-33x+20 = 10x^{2}-8x-25x+20 $$

Step 8: Apply factoring by grouping. Factor $ 2x $ out of the first two terms and $ -5 $ out of the last two terms.

$$ 10x^{2}-8x-25x+20 = 2x\left(5x-4\right) -5\left(5x-4\right) = \left(2x-5\right) \left(5x-4\right) $$

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