Question

How do you long divide `(-x^5 + 3x^4 + 4x^2 + 2x - 7)/(x^2 - 5x + 2)`?

Answer 1

Long divide the coefficients to find:

`(x^5+3x^4+4x^2+2x-7)/(x^2-5x+2)`

`= -x^3-2x^2-8x-32+(-142x+57)/(x^2-5x+2)`

Explanation:

I like to just long divide the coefficients, not forgetting to include a `0` for any missing powers of `x` (in this case `x^3` in the dividend).

The process is similar to long division of numbers.

The result is a quotient `-x^3-2x^2-8x-32` and remainder `-142x+57`