Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (22x2 +  33x) +  8

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  4x²+33x+8 

The first term is,  4x²  its coefficient is  4 .
The middle term is,  +33x  its coefficient is  33 .
The last term, "the constant", is  +8 

Step-1 : Multiply the coefficient of the first term by the constant   4 • 8 = 32 

Step-2 : Find two factors of  32  whose sum equals the coefficient of the middle term, which is   33 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  1  and  32 
                     4x² + 1x + 32x + 8

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 :
                    8 • (4x+1)
Step-5 : Add up the four terms of step 4 :
                    (x+8)  •  (4x+1)
             Which is the desired factorization

Final result :

  (4x + 1) • (x + 8)