Question

How do you divide `6x^4+x^3+1 div 2x^2-2`?

Answer 1

`((x^2-x+1)(6x+1))/(2(x-1))`

Explanation:

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

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

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

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

`=(color(red)cancelcolor(black)((x+1))(x^2-x+1)(6x+1))/(2color(red)cancelcolor(black)((x+1))(x-1))`

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