Perform the indicated operation. 2x^2 + x - 3/9 . (x + 1)^2/2x^2 + 5x + 3=

      x + 3

 ——————

 2x + 1

Step-by-step explanation:

Factoring  2x2 - 5x - 3  

The first term is,  2x2  its coefficient is  2 .

The middle term is,  -5x  its coefficient is  -5 .

The last term, "the constant", is  -3  

Step-1 : Multiply the coefficient of the first term by the constant   2 • -3 = -6  

Step-2 : Find two factors of  -6  whose sum equals the coefficient of the middle term, which is   -5 .

     -6    +    1    =    -5    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -6  and  1  

                    2x2 - 6x + 1x - 3

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

                   2x • (x-3)

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

                    1 • (x-3)

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

                   (2x+1)  •  (x-3)

            Which is the desired factorization