Solution - Simplification or other simple results

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "x5"   was replaced by   "x^5". 

Step  1  :

Equation at the end of step  1  :

  (2 • (x2)) -  3x5
 Step  2  :

Equation at the end of step  2  :

  2x2 -  3x5

Step  3  :

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   2x² - 3x⁵  =   -x² • (3x³ - 2) 

Trying to factor as a Difference of Cubes:

 4.2      Factoring:  3x³ - 2 

Theory : A difference of two perfect cubes,  a³ - b³ can be factored into
              (a-b) • (a² +ab +b²)

Proof :  (a-b)•(a²+ab+b²) =
            a³+a²b+ab²-ba²-b²a-b³ =
            a³+(a²b-ba²)+(ab²-b²a)-b³ =
            a³+0+0-b³ =
            a³-b³

Check :  3  is not a cube !!

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

Polynomial Roots Calculator :

 4.3    Find roots (zeroes) of :       F(x) = 3x³ - 2
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  3  and the Trailing Constant is  -2.

 The factor(s) are:

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

 Let us test ....

Polynomial Roots Calculator found no rational roots

Final result :

  -x2 • (3x3 - 2)