Took much more time

Algebra Level 4

The remainder obtained by dividing the polynomial $x^{100}$ by the polynomial $x^2 -3x+2$ is equal to

[2^{100} +1]x- 2[2^{99} +1]

[2^{100} +1]x

[2^{100} +1]x- 2[2^{99}]

[2^{100} -1 ]x- 2[2^{99} -1 ]

[2^{100} -1]x- 2[2^{99} +1]

[2^{100} +1]x+ 2[2^{99} +1]