Question

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

Answer 1

`x-3`

Explanation:

There is an easier way to do this if we realize `x^3-3x^2+4x-12` can be factored by grouping:

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

Therefore

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