Answer
$x^{3}+4x^{2}+16x+64$
Work Step by Step
Dividing with $x-c\qquad...\qquad c=4.$
Don't forget to place 0's for the missing terms.
$\begin{array}{rrrrrrrr}
\underline{4}| &1 & 0 & 0 & 0 & -256 & & & \\
& & 4 & 16 & 64 & 256 & & & \\
& --& -- &-- &-- &-- & & & \\
&1 & 4 & 16 & 64 & 0 & & & \end{array}$
Quotient = $ x^{3}+4x^{2}+16x+64$
Remainder = $0$
$\displaystyle \frac{dividend}{divisor}=quotient+\frac{remainder}{divisor}$
$\displaystyle \frac{x^{4}-256}{x-4}$ = $x^{3}+4x^{2}+16x+64$
