Question

What are the real solutions

Answer 1

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

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

     -2   +   1   =   -1     -1   +   2   =   1   That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -1  and  2 
                     x2 - 1x + 2x - 2

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

Final result : (x + 2) • (x - 1) • (x - 3) • (2x - 5)