Question

Solve and tell the value of x.
2x²+2x+x+1=120​

Answer 1

Answer:

Step-1 : Multiply the coefficient of the first term by the constant   2 • -120 = -240 

Step-2 : Find two factors of  -240  whose sum equals the coefficient of the middle term, which is   -1 .

     -240   +   1   =   -239 

    -120   +   2   =   -118     

-80   +   3   =   -77   

  -60   +   4   =   -56    

 -48   +   5   =   -43

     -40   +   6   =   -34  

   -30   +   8   =   -22     

-24   +   10   =   -14   

  -20   +   12   =   -8    

 -16   +   15   =   -1   That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -16  and  15 

                     2x2 - 16x + 15x - 120

Step-4 : Add up the first 2 terms, pulling out like factors :

                    2x • (x-8)

              Add up the last 2 terms, pulling out common factors :

                    15 • (x-8)

Step-5 : Add up the four terms of step 4 :

                    (2x+15)  •  (x-8)

             Which is the desired factorization

Step-by-step explanation:

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