Answer
quotient $6x^2+3x-1$ and remainder $r(x)=\frac{-3x+1}{3x^2+1}$
Work Step by Step
Step 1. Using long division as shown in the figure, we can obtain $\frac{18x^4+9x^3+3x^2}{3x^2+1}=6x^2+3x-1+\frac{-3x+1}{3x^2+1}$
Step 2. We can identify the quotient as $6x^2+3x-1$ and the remainder as $r(x)=\frac{-3x+1}{3x^2+1}$
