Answer
quotient $2x^2+3x-1$, remainder $0$
Work Step by Step
Step 1. Using long division as shown in the figure, we have $\frac{4x^4+6x^3+3x-1}{2x^2+1}=2x^2+3x-1+\frac{0}{5x-3}$
Step 2. We can identify the quotient as $2x^2+3x-1$ and the remainder as $0$