Question

How do you divide `(x^4 - 8x^3 + 4x^2 + 12x)/(x^2-2x+2)`?

Answer 1

`(x^4-8x^3+4x^2+12x)/(x^2-2x+2) = (x^2-6x-10)` with remainder `4x+20`.

Explanation:

I like to just long divide the coefficients, not forgetting to include `0`'s for any missing powers of `x`. In our example, that means the constant term of the dividend...

The process is similar to long division of numbers.

The result `1, -6, -10` means `x^2-6x-10` and remainder `4, 20` means `4x+20`

So:

`x^4-8x^3+4x^2+12x = (x^2-2x+2)(x^2-6x-10)+(4x+20)`

Or if you prefer:

`(x^4-8x^3+4x^2+12x)/(x^2-2x+2) = (x^2-6x-10)+(4x+20)/(x^2-2x+2)`