Question

Simplify
a²+ 3 at 2 x a2-7a6
a2-4a-12
a 2.4​

Answer 1

Answer:

1.1     Factoring  a2-4a-12 

The first term is,  a2  its coefficient is  1 .

The middle term is,  -4a  its coefficient is  -4 .

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   -4 .

     -12   +   1   =   -11     -6   +   2   =   -4   That's it

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

                     a2 - 6a + 2a - 12

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

                    a • (a-6)

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

                    2 • (a-6)

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

                    (a+2)  •  (a-6)

             Which is the desired factorization

Final result :

(a + 2) • (a - 6)