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Using long division:
x^2 + (-4x) + 11
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x^2+x-3 /x^4 + (-3x^3) + 4x^2 + (-x) + 1
x^4 + x^3 + (-3x^2)
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-4x^3 + 7x^2 + (-x)
-4x^3 + (-4x^2) + 12x
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11x^2 + (-13x) + 1
11x^2 + 11x + (-33)
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-24x + 34