Answer
quotient $x^2-4x+1$ and remainder $r(x)=\frac{4x-1}{2x^3+1}$
Work Step by Step
Step 1. Using long division as shown in the figure, we can obtain $\frac{2x^5-8x^4+2x^3+x^2}{2x^3+1}=x^2-4x+1+\frac{4x-1}{2x^3+1}$
Step 2. We can identify the quotient as $x^2-4x+1$ and the remainder as $r(x)=\frac{4x-1}{2x^3+1}$
