How to do this by dividing and factoring

Question

(X^2-10x + 25)/(X-5)

Answer 1

Solution erased. The same problem was posted twice in a row !!!

Answer 2

(x² - 10x + 25) / (x-5)

 

In general

 

(x + a)² = x² + 2ax + a²

 

Let a² = 25 = 5² and (-5)²

 

Try a=-5

 

a² = (-5)(-5) = +25

 

2ax = (2)(-5)(x) = -10x

 

Hence x² - 10x + 25 = (x-5)²

 

(x² - 10x + 25)/(x-5) = (x-5)²/(x-5) = (x-5)