#### Answer

quotient $x^4+7x^3+21x^2+60x+182$ and remainder $r(x)=\frac{549}{x-3}$

#### Work Step by Step

Step 1. The coefficients of the dividend can be identified as $\{1,4,0,-3,2, 3\}$ and the divisor is $x-3$; use synthetic division as shown in the figure to get the quotient and the remainder.
Step 2. We can identify the result as $\frac{x^5+4x^3-3x^2+2x+3}{x-3}=x^4+7x^3+21x^2+60x+182+\frac{549}{x-3}$ with the quotient as $x^4+7x^3+21x^2+60x+182$ and the remainder as $r(x)=\frac{549}{x-3}$