Question

How do you divide something like this?

Answer 1

So
`(x^2-12x+8)/(x-5)=(x-7)+(-27)/(x-5)`

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
`(x^2-12x+8)/(x-5)=(x-7)+(-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.