Answer
quotient $4x^2+x+4$ and remainder $r(x)=\frac{3}{x-1}$
Work Step by Step
Step 1. The coefficients of the dividend can be identified as $\{4,-3,3 -1\}$ and the divisor as $x-1$; use synthetic division as shown in the figure to get the quotient and the remainder.
Step 2. We can identify the result as $\frac{4x^3-3x^2+3x-1}{x-1}=4x^2+x+4+\frac{3}{x-1}$ with the quotient as $4x^2+x+4$ and the remainder as $r(x)=\frac{3}{x-1}$
