Question

Solve and show steps! (x^2 - x - 12) / (x-4)

Answer 1

Answer:

x+3

Step-by-step explanation:

           x2 - x - 12

Simplify   ———————————

              x - 4    

Trying to factor by splitting the middle term

1.1     Factoring  x2 - x - 12  

The first term is,  x2  its coefficient is  1 .

The middle term is,  -x  its coefficient is  -1 .

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   -1 .

     -12    +    1    =    -11  

     -6    +    2    =    -4  

     -4    +    3    =    -1    That's it

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

                    x2 - 4x + 3x - 12

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

                   x • (x-4)

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

                   3 • (x-4)

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

                   (x+3)  •  (x-4)

            Which is the desired factorization

Canceling Out :

1.2    Cancel out  (x-4)  which appears on both sides of the fraction line.

Final result :

 x + 3