Question

How to do middle term splitting in algebra?

Answer 1

perhaps it is the quadratic expression factorization problem.

        a x² + b x + c 
  Find factors of  product  a * c..    in such a way that their sum is - b

            x² - 5 x  + 4
   factors or  1 * 4 =  1, 2, 4.            choose  1 and 4
   split the middle term as  - 4 x and  - x
           X² - 4 x - x + 4
             X (X - 4)  - 1 (X - 4)
                   (X-1) (X-4)
       ==========================
             2 x² +  x - 10
     factors of  2 * -10 are  1, 2, 3, 4, 5, 10, 20, -1, -2, -4, -5, -10, -20
                     If u add -4 and 5 you get +1.

           2 x² - 4 x + 5 x - 10
           2 x ( x -2)  + 5 ( x - 2)          =>    (2 x + 5 ) ( x - 2 )

Answer 2

a x² + b x + c  

Multiply a and c in such a way that we got the sum b .