Question

How do you divide `( x^4-2x^3-2x^2+11x+12)/(2x-6)`?

Answer 1

Long divide coefficients to find:

`(x^4-2x^3-2x^2+11x+12)/(2x-6) = 1/2x^3+1/2x^2+1/2x+7`

with remainder `27`

Explanation:

I like to long divide coefficients, but first note that `2x-6 = 2(x-3)`, so to simplify the calculation, let's divide by `x-3`, then divide the result (and any remainder) by `2` at the end:

We find:

`(x^4-2x^3-2x^2+11x+12)/(x-3) = x^3+x^2+x+14`

with remainder `54`.

Hence (dividing by `2`):

`(x^4-2x^3-2x^2+11x+12)/(2x-6) = 1/2x^3+1/2x^2+1/2x+7`

with remainder `27`