Hi all, I have the following Polynomial Division question and not sure if I'm heading in the right direction with it. Its getting more complicated than my lessons have shown but here goes

$\displaystyle 3x^3- 5x^2 +10x +4 / 3x+1$

So I've divided the highest power of $\displaystyle 3x^3$ by 3x and got $\displaystyle x^2$ which I've put above the $\displaystyle 5x^2$

I've then multiplied the $\displaystyle x^2$ by 3x + 1 to get $\displaystyle 3x^3 + x^2$ and added this underneath and subtracted to give me a new remainder of $\displaystyle -4x^2 +10x +4$

I've then taken the highest power of the remainder ($\displaystyle -4x^2$) and divided by highest power of the divisor (3x) which gives me $\displaystyle \frac{4x}{3}$

I'm almost certain this is getting to complicated and thus I've gone wrong somewhere. Would someone mind letting me know if I'm on the right path please?

Thanks