Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((x3) -  22x2) -  32x

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   x³ - 4x² - 32x  =   x • (x² - 4x - 32) 

Trying to factor by splitting the middle term

 3.2     Factoring  x² - 4x - 32 

The first term is,  x²  its coefficient is  1 .
The middle term is,  -4x  its coefficient is  -4 .
The last term, "the constant", is  -32 

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

Step-2 : Find two factors of  -32  whose sum equals the coefficient of the middle term, which is   -4 .

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

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (x-8)
              Add up the last 2 terms, pulling out common factors :
                    4 • (x-8)
Step-5 : Add up the four terms of step 4 :
                    (x+4)  •  (x-8)
             Which is the desired factorization

Final result :

  x • (x + 4) • (x - 8)