Solution - Simplification or other simple results

Step  1  :

Trying to factor by splitting the middle term

 1.1     Factoring  p²+8p+15 

The first term is,  p²  its coefficient is  1 .
The middle term is,  +8p  its coefficient is  8 .
The last term, "the constant", is  +15 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 15 = 15 

Step-2 : Find two factors of  15  whose sum equals the coefficient of the middle term, which is   8 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  3  and  5 
                     p² + 3p + 5p + 15

Step-4 : Add up the first 2 terms, pulling out like factors :
                    p • (p+3)
              Add up the last 2 terms, pulling out common factors :
                    5 • (p+3)
Step-5 : Add up the four terms of step 4 :
                    (p+5)  •  (p+3)
             Which is the desired factorization

Final result :

  (p + 5) • (p + 3)