Solution - Simplification or other simple results

Step  1  :

Trying to factor by splitting the middle term

 1.1     Factoring  n²+241n-9972 

The first term is,  n²  its coefficient is  1 .
The middle term is,  +241n  its coefficient is  241 .
The last term, "the constant", is  -9972 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -9972 = -9972 

Step-2 : Find two factors of  -9972  whose sum equals the coefficient of the middle term, which is   241 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -36  and  277 
                     n² - 36n + 277n - 9972

Step-4 : Add up the first 2 terms, pulling out like factors :
                    n • (n-36)
              Add up the last 2 terms, pulling out common factors :
                    277 • (n-36)
Step-5 : Add up the four terms of step 4 :
                    (n+277)  •  (n-36)
             Which is the desired factorization

Final result :

  (n + 277) • (n - 36)