Solution - Simplification or other simple results

Step  1  :

Trying to factor by splitting the middle term

 1.1     Factoring  x²-4x-21 

The first term is,  x²  its coefficient is  1 .
The middle term is,  -4x  its coefficient is  -4 .
The last term, "the constant", is  -21 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -21 = -21 

Step-2 : Find two factors of  -21  whose sum equals the coefficient of the middle term, which is   -4 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -7  and  3 
                     x² - 7x + 3x - 21

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (x-7)
              Add up the last 2 terms, pulling out common factors :
                    3 • (x-7)
Step-5 : Add up the four terms of step 4 :
                    (x+3)  •  (x-7)
             Which is the desired factorization

Final result :

  (x + 3) • (x - 7)