Solution - Simplification or other simple results

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "x9"   was replaced by   "x^9". 

Step  1  :

Equation at the end of step  1  :

  (9 • (x2)) -  (2•32x9)
 Step  2  :

Equation at the end of step  2  :

  32x2 -  (2•32x9)

Step  3  :

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   9x² - 18x⁹  =   -9x² • (2x⁷ - 1) 

Polynomial Roots Calculator :

 4.2    Find roots (zeroes) of :       F(x) = 2x⁷ - 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 :

  -9x2 • (2x7 - 1)