Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

Step  2  :

            3x2 - 110
 Simplify   —————————
              x - 2  

Trying to factor as a Difference of Squares :

 2.1      Factoring:  3x² - 110 

Theory : A difference of two perfect squares,  A² - B²  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =
         A² - AB + BA - B² =
         A² - AB + AB - B² =
         A² - B²

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check :  3  is not a square !!

Ruling : Binomial can not be factored as the
difference of two perfect squares

Polynomial Long Division :

 2.2    Polynomial Long Division
Dividing :  3x² - 110 
                              ("Dividend")
By         :    x - 2    ("Divisor")

Quotient :  3x + 6 
Remainder :  -98 

Final result :

  3x2 - 110
  —————————
    x - 2