Solution - Simplification or other simple results

Step  1  :

Trying to factor by splitting the middle term

 1.1     Factoring  u²-2u-3 

The first term is,  u²  its coefficient is  1 .
The middle term is,  -2u  its coefficient is  -2 .
The last term, "the constant", is  -3 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -3 = -3 

Step-2 : Find two factors of  -3  whose sum equals the coefficient of the middle term, which is   -2 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -3  and  1 
                     u² - 3u + 1u - 3

Step-4 : Add up the first 2 terms, pulling out like factors :
                    u • (u-3)
              Add up the last 2 terms, pulling out common factors :
                     1 • (u-3)
Step-5 : Add up the four terms of step 4 :
                    (u+1)  •  (u-3)
             Which is the desired factorization

Final result :

  (u + 1) • (u - 3)