Decomposition factor: (x-a) ^ 2 - (X-B) ^ 2 =?; X + 2x ^ 2 + x ^ 3 =?; 5x ^ 3-10x ^ 2 + 5x =?

Decomposition factor: (x-a) ^ 2 - (X-B) ^ 2 =?; X + 2x ^ 2 + x ^ 3 =?; 5x ^ 3-10x ^ 2 + 5x =?

The first is the square difference formula: = [(x-a) + (X-B)] [(x-a) - (X-B)]
The second extraction common factor X: the original formula = x (1 + 2x + x ^ 2) = x (1 + x) ^ 2
The third extraction common factor 5x: the original formula = 5x (x ^ 2-2x + 1) = 5x (x-1) ^ 2
Go go go

Find the minimum value of 5x ^ 2-10x + 10 / x ^ 2-2x + 3

Next time, please add brackets to show it!
First 5x ^ 2-10x + 10 Put forward the common factor "5" to get 5 * (x ^ 2-2x + 2) ②
We'll find that it's very similar to the following! Let's change formula 2 into 5 * (x ^ 2-2x + 3-1) ③
5*（x^2-2X+3）-5………… ④
Divide x ^ 2-2x + 3 by 4 to get 5 - (5 / x ^ 2-2x + 3)
Just ask (5 / x ^ 2-2x + 3) to get the minimum value of x ^ 2-2x + 3! The result is 5 / 2