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Algebra Level 4

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

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