Solution - Simplification or other simple results

Step  1  :

Trying to factor by splitting the middle term

 1.1     Factoring  a²-27a+50 

The first term is,  a²  its coefficient is  1 .
The middle term is,  -27a  its coefficient is  -27 .
The last term, "the constant", is  +50 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 50 = 50 

Step-2 : Find two factors of  50  whose sum equals the coefficient of the middle term, which is   -27 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -25  and  -2 
                     a² - 25a - 2a - 50

Step-4 : Add up the first 2 terms, pulling out like factors :
                    a • (a-25)
              Add up the last 2 terms, pulling out common factors :
                    2 • (a-25)
Step-5 : Add up the four terms of step 4 :
                    (a-2)  •  (a-25)
             Which is the desired factorization

Final result :

  (a - 2) • (a - 25)