Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((22x2 -  9x) -  8) +  5x

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   4x² - 4x - 8  =   4 • (x² - x - 2) 

Trying to factor by splitting the middle term

 3.2     Factoring  x² - x - 2 

The first term is,  x²  its coefficient is  1 .
The middle term is,  -x  its coefficient is  -1 .
The last term, "the constant", is  -2 

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

Step-2 : Find two factors of  -2  whose sum equals the coefficient of the middle term, which is   -1 .

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

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 :
                     1 • (x-2)
Step-5 : Add up the four terms of step 4 :
                    (x+1)  •  (x-2)
             Which is the desired factorization

Final result :

  4 • (x + 1) • (x - 2)