Answer
quotient $x^3+4x^2+16x+64$ and remainder $r(x)=0$
Work Step by Step
Step 1. The coefficients of the dividend can be identified in order as $\{1,0,0,0,-256\}$ and the divisor is $x-4$; use synthetic division as shown in the figure to get the quotient and the remainder.
Step 2. We can identify the result as $\frac{x^4-256}{x-4}=x^3+4x^2+16x+64+\frac{0}{x-4}$ with the quotient as $x^3+4x^2+16x+64$ and the remainder as $r(x)=0$