Question

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

Answer 1

SOLUTION

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

$\frac{2x^4+5x^2-21x+24}{x^2+2x+4}$

The expression above can be properly written as

$\frac{2x^4+0x^3+5x^2-21x+24}{x^2+2x+4}$

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

$2x^2-4x+5+\frac{-15x+4}{x^2+2x+4}$