Solution - Simplification or other simple results

Step  1  :

Trying to factor by splitting the middle term

 1.1     Factoring  x²-15x+56 

The first term is,  x²  its coefficient is  1 .
The middle term is,  -15x  its coefficient is  -15 .
The last term, "the constant", is  +56 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 56 = 56 

Step-2 : Find two factors of  56  whose sum equals the coefficient of the middle term, which is   -15 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -8  and  -7 
                     x² - 8x - 7x - 56

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (x-8)
              Add up the last 2 terms, pulling out common factors :
                    7 • (x-8)
Step-5 : Add up the four terms of step 4 :
                    (x-7)  •  (x-8)
             Which is the desired factorization

Final result :

  (x - 7) • (x - 8)