Solution - Simplification or other simple results

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "n2"   was replaced by   "n^2".  2 more similar replacement(s).

Step  1  :

Equation at the end of step  1  :

  (((16•(n4))-(8•(n3)))+23n2)-4n
 Step  2  :

Equation at the end of step  2  :

  (((16 • (n4)) -  23n3) +  23n2) -  4n
 Step  3  :

Equation at the end of step  3  :

  ((24n4 -  23n3) +  23n2) -  4n

Step  4  :

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   16n⁴ - 8n³ + 8n² - 4n  = 

  4n • (4n³ - 2n² + 2n - 1) 

Checking for a perfect cube :

 5.2    4n³ - 2n² + 2n - 1  is not a perfect cube

Trying to factor by pulling out :

 5.3      Factoring:  4n³ - 2n² + 2n - 1 

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

Group 1:  2n - 1 
Group 2:  4n³ - 2n² 

Pull out from each group separately :

Group 1:   (2n - 1) • (1)
Group 2:   (2n - 1) • (2n²)
               -------------------
Add up the two groups :
               (2n - 1)  •  (2n² + 1) 
Which is the desired factorization

Polynomial Roots Calculator :

 5.4    Find roots (zeroes) of :       F(n) = 2n² + 1
Polynomial Roots Calculator is a set of methods aimed at finding values of  n  for which   F(n)=0  

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

  4n • (2n2 + 1) • (2n - 1)