Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((0 -  (x6)) +  (2•5x4)) -  25x

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   -x⁶ + 10x⁴ - 25x  =   -x • (x⁵ - 10x³ + 25) 

Polynomial Roots Calculator :

 3.2    Find roots (zeroes) of :       F(x) = x⁵ - 10x³ + 25
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  1  and the Trailing Constant is  25.

 The factor(s) are:

of the Leading Coefficient :  1
 of the Trailing Constant :  1 ,5 ,25

 Let us test ....

Polynomial Roots Calculator found no rational roots

Final result :

  -x • (x5 - 10x3 + 25)