Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (2x2 +  12x) +  16

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   2x² + 12x + 16  =   2 • (x² + 6x + 8) 

Trying to factor by splitting the middle term

 3.2     Factoring  x² + 6x + 8 

The first term is,  x²  its coefficient is  1 .
The middle term is,  +6x  its coefficient is  6 .
The last term, "the constant", is  +8 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 8 = 8 

Step-2 : Find two factors of  8  whose sum equals the coefficient of the middle term, which is   6 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  2  and  4 
                     x² + 2x + 4x + 8

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

Final result :

  2 • (x + 4) • (x + 2)