Question

How do you long divide `(6x^4-3x^3+5x^2+2x-6)/(3x^2-2)`?

Answer 1

`(6x^4 – 3x^3 + 5x^2 +2x -6)/(3x^2-2) = 2x^2 –x +3`

Explanation:

You use the process of long division, but you have to leave gaps for the missing powers of `x`.

So,

`(6x^4 – 3x^3 + 5x^2 +2x -6)/(3x^2-2) = 2x^2 –x +3`

Check:

`(3x^2-2)( 2x^2 –x +3)= 6x^4 – 3x^3 + 9x^2 -4x^2 +2x -6 = 6x^4 – 3x^3 + 5x^2 + 2x -6`