Solution - Simplification or other simple results

Step  1  :

            f2 + 7f + 10
 Simplify   ————————————
               f + 2    

Trying to factor by splitting the middle term

 1.1     Factoring  f² + 7f + 10 

The first term is,  f²  its coefficient is  1 .
The middle term is,  +7f  its coefficient is  7 .
The last term, "the constant", is  +10 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 10 = 10 

Step-2 : Find two factors of  10  whose sum equals the coefficient of the middle term, which is   7 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  2  and  5 
                     f² + 2f + 5f + 10

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

Canceling Out :

 1.2    Cancel out  (f+2)  which appears on both sides of the fraction line.

Final result :

  f + 5