Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (22x2 +  5x) +  1

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  4x²+5x+1 

The first term is,  4x²  its coefficient is  4 .
The middle term is,  +5x  its coefficient is  5 .
The last term, "the constant", is  +1 

Step-1 : Multiply the coefficient of the first term by the constant   4 • 1 = 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 
                     4x² + 1x + 4x + 1

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

Final result :

  (4x + 1) • (x + 1)