Question

How do you divide `(12x^4-18x^3+36x^2)-:6x^3`?

Answer 1

`2x+3+6/x`

Explanation:

We're dividing a single term, `6x^3`, into a polynomial, so we can take advantage of the following fact which allows us to effectively divide one term into other terms:

`(a+-b)/c=a/c+-b/c`

So,

`(12x^4-18x^3+36x^2)/(6x^3)=(12x^4)/(6x^3)-(18x^3)/(6x^3)+(36x^2)/(6x^3)`

Now, we begin simplifying. Recall that `x^a/x^b=x^(a-b).`

`2x^(4-3)+3x^(3-3)+6x^(2-3)=2x+3+6x^-1=2x+3+6/x`
(As `x^-a=1/x^a`)