Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (2t2 +  36t) +  34

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   2t² + 36t + 34  =   2 • (t² + 18t + 17) 

Trying to factor by splitting the middle term

 3.2     Factoring  t² + 18t + 17 

The first term is,  t²  its coefficient is  1 .
The middle term is,  +18t  its coefficient is  18 .
The last term, "the constant", is  +17 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 17 = 17 

Step-2 : Find two factors of  17  whose sum equals the coefficient of the middle term, which is   18 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  1  and  17 
                     t² + 1t + 17t + 17

Step-4 : Add up the first 2 terms, pulling out like factors :
                    t • (t+1)
              Add up the last 2 terms, pulling out common factors :
                    17 • (t+1)
Step-5 : Add up the four terms of step 4 :
                    (t+17)  •  (t+1)
             Which is the desired factorization

Final result :

  2 • (t + 17) • (t + 1)