Solution - Simplification or other simple results

Step  1  :

Trying to factor by splitting the middle term

 1.1     Factoring  t²-3t-4 

The first term is,  t²  its coefficient is  1 .
The middle term is,  -3t  its coefficient is  -3 .
The last term, "the constant", is  -4 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -4 = -4 

Step-2 : Find two factors of  -4  whose sum equals the coefficient of the middle term, which is   -3 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -4  and  1 
                     t² - 4t + 1t - 4

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

Final result :

  (t + 1) • (t - 4)