Solution - Simplification or other simple results

Step  1  :

Trying to factor by splitting the middle term

 1.1     Factoring  n²-10n+9 

The first term is,  n²  its coefficient is  1 .
The middle term is,  -10n  its coefficient is  -10 .
The last term, "the constant", is  +9 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 9 = 9 

Step-2 : Find two factors of  9  whose sum equals the coefficient of the middle term, which is   -10 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -9  and  -1 
                     n² - 9n - 1n - 9

Step-4 : Add up the first 2 terms, pulling out like factors :
                    n • (n-9)
              Add up the last 2 terms, pulling out common factors :
                     1 • (n-9)
Step-5 : Add up the four terms of step 4 :
                    (n-1)  •  (n-9)
             Which is the desired factorization

Final result :

  (n - 1) • (n - 9)