Solution - Simplification or other simple results

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "h2"   was replaced by   "h^2".  1 more similar replacement(s).

Step  1  :

Equation at the end of step  1  :

  (((h3) -  3) +  h) -  3h2

Step  2  :

Checking for a perfect cube :

 2.1    h³-3h²+h-3  is not a perfect cube

Trying to factor by pulling out :

 2.2      Factoring:  h³-3h²+h-3 

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

Group 1:  h-3 
Group 2:  h³-3h² 

Pull out from each group separately :

Group 1:   (h-3) • (1)
Group 2:   (h-3) • (h²)
               -------------------
Add up the two groups :
               (h-3)  •  (h²+1) 
Which is the desired factorization

Polynomial Roots Calculator :

 2.3    Find roots (zeroes) of :       F(h) = h²+1
Polynomial Roots Calculator is a set of methods aimed at finding values of  h  for which   F(h)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  h  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  1.

 The factor(s) are:

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

 Let us test ....

Polynomial Roots Calculator found no rational roots

Final result :

  (h2 + 1) • (h - 3)