Question

How would I use polynomial division to write the rational expression as a polynomial in descending powers?

Answer 1

We want to perform the division and write our answer in descending powers

`(2x^4+5x^2-21x+24)/(x^2+2x+4)`

The expression above can be properly written as

`(2x^4+0x^3+5x^2-21x+24)/(x^2+2x+4)`

Perfoming the division we have

Step 3

Hence the answer in descending powers is

`2x^2-4x+5\text{ Remaider }-15x+4`

It can also be written as

`2x^2-4x+5+(-15x+4)/(x^2+2x+4)`