Question

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

Answer 1

Long divide the coefficients to find:

`(x^4-2x^3-2x^2-2x+3)/(x^2-3) = x^2-2x+1+(-8x+6)/(x^2-3)`

Explanation:

I like to long divide the coefficients like this:

Note that the divisor is written `1, 0, -3`, including a `0` for the coefficient of the term in `x`.

Write the dividend under the bar and the divisor to the left.

Write the quotient term-by-term above the bar, choosing each digit so that when multiplied by the divisor it matches the leading term of your running remainder. Once the remainder is too short to allow further division, you are finished.

The quotient represented by `1, -2, 1` is `x^2-2x+1` and the remainder `-8x+6`