Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (((3•(r4))-(2•(r3)))+(2•3r2))-4r
 Step  2  :

Equation at the end of step  2  :

  (((3 • (r4)) -  2r3) +  (2•3r2)) -  4r
 Step  3  :

Equation at the end of step  3  :

  ((3r4 -  2r3) +  (2•3r2)) -  4r

Step  4  :

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   3r⁴ - 2r³ + 6r² - 4r  = 

  r • (3r³ - 2r² + 6r - 4) 

Checking for a perfect cube :

 5.2    3r³ - 2r² + 6r - 4  is not a perfect cube

Trying to factor by pulling out :

 5.3      Factoring:  3r³ - 2r² + 6r - 4 

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

Group 1:  6r - 4 
Group 2:  3r³ - 2r² 

Pull out from each group separately :

Group 1:   (3r - 2) • (2)
Group 2:   (3r - 2) • (r²)
               -------------------
Add up the two groups :
               (3r - 2)  •  (r² + 2) 
Which is the desired factorization

Polynomial Roots Calculator :

 5.4    Find roots (zeroes) of :       F(r) = r² + 2
Polynomial Roots Calculator is a set of methods aimed at finding values of  r  for which   F(r)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  r  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  2.

 The factor(s) are:

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

 Let us test ....

Polynomial Roots Calculator found no rational roots

Final result :

  r • (r2 + 2) • (3r - 2)