Solution - Simplification or other simple results

Step  1  :

Trying to factor by splitting the middle term

 1.1     Factoring  x²-14x-51 

The first term is,  x²  its coefficient is  1 .
The middle term is,  -14x  its coefficient is  -14 .
The last term, "the constant", is  -51 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -51 = -51 

Step-2 : Find two factors of  -51  whose sum equals the coefficient of the middle term, which is   -14 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -17  and  3 
                     x² - 17x + 3x - 51

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (x-17)
              Add up the last 2 terms, pulling out common factors :
                    3 • (x-17)
Step-5 : Add up the four terms of step 4 :
                    (x+3)  •  (x-17)
             Which is the desired factorization

Final result :

  (x + 3) • (x - 17)