Solution - Simplification or other simple results

Step  1  :

Trying to factor by splitting the middle term

 1.1     Factoring  x²+3x-40 

The first term is,  x²  its coefficient is  1 .
The middle term is,  +3x  its coefficient is  3 .
The last term, "the constant", is  -40 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -40 = -40 

Step-2 : Find two factors of  -40  whose sum equals the coefficient of the middle term, which is   3 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -5  and  8 
                     x² - 5x + 8x - 40

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (x-5)
              Add up the last 2 terms, pulling out common factors :
                    8 • (x-5)
Step-5 : Add up the four terms of step 4 :
                    (x+8)  •  (x-5)
             Which is the desired factorization

Final result :

  (x + 8) • (x - 5)