Step-by-step explanation:

The first TERM is,  x^2  its coefficient is  1 .

The middle term is,  -8x  its coefficient is  -8 .

The last term, "the CONSTANT", is  +12 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 12 = 12 

Step-2 : Find two factors of  12  WHOSE sum equals the coefficient of the middle term, which is   -8 .

-6   +   -2   =   -8   That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -6  and  -2 

                     x2 - 6x - 2x - 12

Step-4 : Add up the first 2 TERMS, pulling out like factors :

                    x • (x-6)

              Add up the last 2 terms, pulling out common factors :

                    2 • (x-6)

Step-5 : Add up the four terms of step 4 :

                    (x-2)  •  (x-6)

             Which is the desired factorization

x= 2 or x= 6.

relationship between zeros and coefficent of polynomial..

α+β = -b/a.

αβ =c/a.

sum of zeroes =-b/a

so,2+6 = -(-8)/1

8=8.

product of zeroes =c/a .

(2)(6) = 12/1.

12 = 12.