Question

How do you long divide `(x^4 )/(x^3+x²+5x+3)`?

Answer 1

See explanation...

Explanation:

You can long divide polynomials in a similar way to the way you long divide numbers.

or you can just long divide the coefficients like this:

In both cases, we find:

`x^4 / (x^3+x^2+5x+3) = x - 1`

with remainder `-4x^2+2x+3`

One thing to watch out for when dividing polynomials in these ways (especially the second way), is to make sure that you include a term with `0` coefficient if any power of `x` is 'missing'.

For example, when dividing by `x^2 - 1`, the coefficients are `1, 0, -1` not just `1, -1`.

Here's another example where I animated the process...