Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  
 Step  2  :

Equation at the end of step  2  :

Step  3  :

            3x3 - 3x2 - 18x
 Simplify   ———————————————
              x2 - x - 6   

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   3x³ - 3x² - 18x  =   3x • (x² - x - 6) 

Trying to factor by splitting the middle term

 4.2     Factoring  x² - x - 6 

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

Step-1 : Multiply the coefficient of the first term by the constant   1 • -6 = -6 

Step-2 : Find two factors of  -6  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,  -3  and  2 
                     x² - 3x + 2x - 6

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (x-3)
              Add up the last 2 terms, pulling out common factors :
                    2 • (x-3)
Step-5 : Add up the four terms of step 4 :
                    (x+2)  •  (x-3)
             Which is the desired factorization

Trying to factor by splitting the middle term

 4.3     Factoring  x²-x-6 

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

Step-1 : Multiply the coefficient of the first term by the constant   1 • -6 = -6 

Step-2 : Find two factors of  -6  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,  -3  and  2 
                     x² - 3x + 2x - 6

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (x-3)
              Add up the last 2 terms, pulling out common factors :
                    2 • (x-3)
Step-5 : Add up the four terms of step 4 :
                    (x+2)  •  (x-3)
             Which is the desired factorization

Canceling Out :

 4.4    Cancel out  (x+2)  which appears on both sides of the fraction line.

Canceling Out :

 4.5    Cancel out  (x-3)  which appears on both sides of the fraction line.

Final result :

  3x