Question 147547
We shall want
g(x)=(-x^3 + 3x^2 - 3x + 1)/(-x+1)

You can solve this a few different ways. I will use long division.
......x^2-2x+1
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-x+1)-x^3 + 3x^2 - 3x + 1
...-(-x^3+x^2)
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........2x^2-3x
......-(2x^2-2x)
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..........-x+1
........-(-x+1)
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.............0

So g(x)=x^2-2x+1