Answer
$x^{6}+2x^{5}+4x^{4}+8x^{3}+16x^{2}+32x+64$
Work Step by Step
Dividing with $x-c\qquad...\qquad c=2.$
Don't forget to place 0's for the missing terms.
$\begin{array}{rrrrrrrr}
\underline{2}| &1 & 0 & 0 & 0 & 0 & 0 & 0 & -128 \\
& & 2 & 4 & 8 & 16 & 32 & 64 & 128 \\
& --& -- &-- &-- &-- & --& -- & -- \\
&1 & 2 & 4 & 8 & 16 & 32 & 64 & 0 \end{array}$
Quotient = $ x^{6}+2x^{5}+4x^{4}+8x^{3}+16x^{2}+32x+64$
Remainder = $0$
$\displaystyle \frac{dividend}{divisor}=quotient+\frac{remainder}{divisor}$
$\displaystyle \frac{x^{7}-128}{x-2}$ = $x^{6}+2x^{5}+4x^{4}+8x^{3}+16x^{2}+32x+64$
