Question

middle term split x^2-5x+1=0

Answer 1

x²  - 5 x  + 6  =  x² - 3 x  -2 x + 6  =  x (x -3)  -2 (x -3) 
= (x-2) (x-3)

Answer 2

Step by step solution : Step  1  :Simplify 2x2-5x - 3 Trying to factor by splitting the middle term 1.1     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)
Now add up the four terms of step 3 :
                    (2x+1)  •  (x-3)
Which is the desired factorization