Question

How do you divide something like this?

Answer 1

Answer:

So $\frac{x^2-12x+8}{x-5}=(x-7)+\frac{-27}{x-5}$

Step-by-step explanation:

Since we are dividing by a linear factor, I'm going to use synthetic division.

Since the linear factor that we are dividing by is (x-5), I'm going to put 5 on the outside:

5    |     1       -12       8

      |              5      -35

      |--------------------------

           1         -7      -27

So the quotient x-7 while the remainder is -27.

So $\frac{x^2-12x+8}{x-5}=(x-7)+\frac{-27}{x-5}$

You could do long division if you prefer:

           x-7

         ------------------------

(x-5) |   x^2-12x+8

        - (x^2-5x)

        --------------------------

                -7x+8

              -(-7x+35)

         ---------------------

                     -27

You still get the same thing that the quotient is x-7 and the remainder is -27.