Solution - Simplification or other simple results

Step  1  :

Trying to factor by splitting the middle term

 1.1     Factoring  y²+12y+11 

The first term is,  y²  its coefficient is  1 .
The middle term is,  +12y  its coefficient is  12 .
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   12 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  1  and  11 
                     y² + 1y + 11y + 11

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

Final result :

  (y + 11) • (y + 1)