Solution - Simplification or other simple results

Step  1  :

Trying to factor by splitting the middle term

 1.1     Factoring  k²-13k+40 

The first term is,  k²  its coefficient is  1 .
The middle term is,  -13k  its coefficient is  -13 .
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   -13 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -8  and  -5 
                     k² - 8k - 5k - 40

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

Final result :

  (k - 5) • (k - 8)