Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (2n2 +  5n) +  2

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  2n²+5n+2 

The first term is,  2n²  its coefficient is  2 .
The middle term is,  +5n  its coefficient is  5 .
The last term, "the constant", is  +2 

Step-1 : Multiply the coefficient of the first term by the constant   2 • 2 = 4 

Step-2 : Find two factors of  4  whose sum equals the coefficient of the middle term, which is   5 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  1  and  4 
                     2n² + 1n + 4n + 2

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

Final result :

  (2n + 1) • (n + 2)