Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (((2 • (p3)) +  5p2) +  6p) +  15
 Step  2  :

Equation at the end of step  2  :

  ((2p3 +  5p2) +  6p) +  15

Step  3  :

Checking for a perfect cube :

 3.1    2p³+5p²+6p+15  is not a perfect cube

Trying to factor by pulling out :

 3.2      Factoring:  2p³+5p²+6p+15 

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

Group 1:  6p+15 
Group 2:  2p³+5p² 

Pull out from each group separately :

Group 1:   (2p+5) • (3)
Group 2:   (2p+5) • (p²)
               -------------------
Add up the two groups :
               (2p+5)  •  (p²+3) 
Which is the desired factorization

Polynomial Roots Calculator :

 3.3    Find roots (zeroes) of :       F(p) = p²+3
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  3.

 The factor(s) are:

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

 Let us test ....

Polynomial Roots Calculator found no rational roots

Final result :

  (p2 + 3) • (2p + 5)