Solution - Simplification or other simple results

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "t2"   was replaced by   "t^2".  1 more similar replacement(s).

Step  1  :

Equation at the end of step  1  :

  (((9 • (t3)) -  32t2) +  2t) -  2
 Step  2  :

Equation at the end of step  2  :

  ((32t3 -  32t2) +  2t) -  2

Step  3  :

Checking for a perfect cube :

 3.1    9t³-9t²+2t-2  is not a perfect cube

Trying to factor by pulling out :

 3.2      Factoring:  9t³-9t²+2t-2 

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  2t-2 
Group 2:  9t³-9t² 

Pull out from each group separately :

Group 1:   (t-1) • (2)
Group 2:   (t-1) • (9t²)
               -------------------
Add up the two groups :
               (t-1)  •  (9t²+2) 
Which is the desired factorization

Polynomial Roots Calculator :

 3.3    Find roots (zeroes) of :       F(t) = 9t²+2
Polynomial Roots Calculator is a set of methods aimed at finding values of  t  for which   F(t)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  t  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  9  and the Trailing Constant is  2.

 The factor(s) are:

of the Leading Coefficient :  1,3 ,9
 of the Trailing Constant :  1 ,2

 Let us test ....

Polynomial Roots Calculator found no rational roots

Final result :

  (9t2 + 2) • (t - 1)