Solution - Simplification or other simple results

Step  1  :

             d
 Simplify   ——
            dx

Canceling Out :

 1.1    Canceling out d as it appears on both sides of the fraction line

Equation at the end of step  1  :

     1                        
  (((— • x3) +  x2) +  x) +  1
     x                        

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  2x²+x+1 

The first term is,  2x²  its coefficient is  2 .
The middle term is,  +x  its coefficient is  1 .
The last term, "the constant", is  +1 

Step-1 : Multiply the coefficient of the first term by the constant   2 • 1 = 2 

Step-2 : Find two factors of  2  whose sum equals the coefficient of the middle term, which is   1 .

Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored

Final result :

  2x2 + x + 1