Answer
quotient $x^6+2x^5+4x^4+8x^3+16x^2+32x+64$ and remainder $r(x)=0$
Work Step by Step
Step 1. The coefficients of the dividend can be identified in order as $\{1,0,0,0,0,0,0,-128\}$ and the divisor is $x-2$; use synthetic division as shown in the figure to get the quotient and the remainder.
Step 2. We can identify the result as $\frac{x^7-128}{x-2}=x^6+2x^5+4x^4+8x^3+16x^2+32x+64+\frac{0}{x-2}$ with the quotient as $x^6+2x^5+4x^4+8x^3+16x^2+32x+64$ and the remainder as $r(x)=0$
