Question

solve algebraic equations : a^2-6a+40

Answer 1

The first term is,  a2  its coefficient is  1 .
The middle term is,  -6a  its coefficient is  -6 .
The last term, "the constant", is  -40 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -40 = -40 

Step-2 : Find two factors of  -40  whose sum equals the coefficient of the middle term, which is   -6 .

     -40   +   1   =   -39     -20   +   2   =   -18     -10   +   4   =   -6   That's it


Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -10  and  4 
                     a2 - 10a + 4a - 40

Step-4 : Add up the first 2 terms, pulling out like factors :
                    a • (a-10)
              Add up the last 2 terms, pulling out common factors :
                    4 • (a-10)
Step-5 : Add up the four terms of step 4 :
                    (a+4)  •  (a-10)
             Which is the desired factorization