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

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

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

the answer is su.k.my? ? co.kc