Step 1 :

After factoring out $ 4x $ we have:

$$ 4x^{3}-220x^{2}+2800x = 4x ( x^{2}-55x+700 ) $$

Step 2 :

Step 2: Identify constants $ \color{blue}{ b }$ and $\color{red}{ c }$. ( $ \color{blue}{ b }$ is a number in front of the $ x $ term and $ \color{red}{ c } $ is a constant). In our case:

$$ \color{blue}{ b = -55 } ~ \text{ and } ~ \color{red}{ c = 700 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ -55 } $ and multiply to $ \color{red}{ 700 } $.

Step 3: Find out pairs of numbers with a product of $\color{red}{ c = 700 }$.

PRODUCT = 700
1     700	-1     -700
2     350	-2     -350
4     175	-4     -175
5     140	-5     -140
7     100	-7     -100
10     70	-10     -70
14     50	-14     -50
20     35	-20     -35
25     28	-25     -28

Step 4: Find out which pair sums up to $\color{blue}{ b = -55 }$

PRODUCT = 700 and SUM = -55
1     700	-1     -700
2     350	-2     -350
4     175	-4     -175
5     140	-5     -140
7     100	-7     -100
10     70	-10     -70
14     50	-14     -50
20     35	-20     -35
25     28	-25     -28

Step 5: Put -20 and -35 into placeholders to get factored form.

$$ \begin{aligned} x^{2}-55x+700 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ x^{2}-55x+700 & = (x -20)(x -35) \end{aligned} $$

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