Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  2 -  ((x3) • (0 -  22x2))
 Step  2  :
 Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   4x⁵ + 2  =   2 • (2x⁵ + 1) 

Polynomial Roots Calculator :

 3.2    Find roots (zeroes) of :       F(x) = 2x⁵ + 1
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  2  and the Trailing Constant is  1.

 The factor(s) are:

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

 Let us test ....

Polynomial Roots Calculator found no rational roots

Final result :

  2 • (2x5 + 1)