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

So I've divided the highest power of by 3x and got which I've put above the 5x^2" alt="5x^2" />

I've then multiplied the by 3x + 1 to get and added this underneath and subtracted to give me a new remainder of

I've then taken the highest power of the remainder ( ) and divided by highest power of the divisor (3x) which gives me \frac{4x}{3}" alt="\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