Solution - Simplification or other simple results

Step  1  :

Trying to factor by splitting the middle term

 1.1     Factoring  p²+p-2 

The first term is,  p²  its coefficient is  1 .
The middle term is,  +p  its coefficient is  1 .
The last term, "the constant", is  -2 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -2 = -2 

Step-2 : Find two factors of  -2  whose sum equals the coefficient of the middle term, which is   1 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -1  and  2 
                     p² - 1p + 2p - 2

Step-4 : Add up the first 2 terms, pulling out like factors :
                    p • (p-1)
              Add up the last 2 terms, pulling out common factors :
                    2 • (p-1)
Step-5 : Add up the four terms of step 4 :
                    (p+2)  •  (p-1)
             Which is the desired factorization

Final result :

  (p + 2) • (p - 1)