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  :

            6x3 - 8x2 - 8x - 13
 Simplify   ———————————————————
                  2x - 2       

Checking for a perfect cube :

 3.1    6x³ - 8x² - 8x - 13  is not a perfect cube

Trying to factor by pulling out :

 3.2      Factoring:  6x³ - 8x² - 8x - 13 

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  6x³ - 13 
Group 2:  -8x² - 8x 

Pull out from each group separately :

Group 1:   (6x³ - 13) • (1)
Group 2:   (x + 1) • (-8x)

Bad news !! Factoring by pulling out fails :

The groups have no common factor and can not be added up to form a multiplication.

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   2x - 2  =   2 • (x - 1) 

Polynomial Roots Calculator :

 4.2    Find roots (zeroes) of :       F(x) = 6x³ - 8x² - 8x - 13
Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  6  and the Trailing Constant is  -13.

 The factor(s) are:

of the Leading Coefficient :  1,2 ,3 ,6
 of the Trailing Constant :  1 ,13

 Let us test ....

Polynomial Roots Calculator found no rational roots

Polynomial Long Division :

 4.3    Polynomial Long Division
Dividing :  6x³ - 8x² - 8x - 13 
                              ("Dividend")
By         :    x - 1    ("Divisor")

Quotient :  6x² - 2x - 10 
Remainder :  -23 

Final result :

  6x3 - 8x2 - 8x - 13
  ———————————————————
      2 • (x - 1)