AHSME 1969 Problem 34

The remainder $R$ obtained by dividing $x^{100}$ by $x^2-3x+2$ is a polynomial of degree less than $2$. Then $R$ may be written as:

$\text{(A) }2^{100}-1 \text{(B) } 2^{100}(x-1)-(x-2) \text{(C) } 2^{200}(x-3) \\ \text{(D) } x(2^{100}-1)+2(2^{99}-1) \text{(E) } 2^{100}(x+1)-(x+2)$