Find the sum of 2x 2 + 3x - 4, 8 - 3x, and -5x 2 + 2.

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 

                     2*x^2-3*x-(2)=0 

 2.1     Factoring  2x2-3x-2 

The first term is,  2x2  its coefficient is  2 .
The middle term is,  -3x  its coefficient is  -3 .
The last term, "the constant", is  -2 

Step-1 : Multiply the coefficient of the first term by the constant   2 • -2 = -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 
                     2x2 - 4x + 1x - 2

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