Solution - Simplification or other simple results

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "p1"   was replaced by   "p^1". 

Step  1  :

Step  2  :

Pulling out like terms :

 2.1     Pull out like factors :

   p³ + p  =   p • (p² + 1) 

Polynomial Roots Calculator :

 2.2    Find roots (zeroes) of :       F(p) = p² + 1
Polynomial Roots Calculator is a set of methods aimed at finding values of  p  for which   F(p)=0  

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

  p • (p2 + 1)