Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (22f2 +  40f) -  44

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   4f² + 40f - 44  =   4 • (f² + 10f - 11) 

Trying to factor by splitting the middle term

 3.2     Factoring  f² + 10f - 11 

The first term is,  f²  its coefficient is  1 .
The middle term is,  +10f  its coefficient is  10 .
The last term, "the constant", is  -11 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -11 = -11 

Step-2 : Find two factors of  -11  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,  -1  and  11 
                     f² - 1f + 11f - 11

Step-4 : Add up the first 2 terms, pulling out like factors :
                    f • (f-1)
              Add up the last 2 terms, pulling out common factors :
                    11 • (f-1)
Step-5 : Add up the four terms of step 4 :
                    (f+11)  •  (f-1)
             Which is the desired factorization

Final result :

  4 • (f + 11) • (f - 1)