Divide the polynomial `f(x)=3x^2-x^3-3x+5` by the polynomial `g(x)=x-1and verify the division algorithm.

Explanation

Write the polynomials in the standard form:

`f(x)=-x^3+3x^2-3x+5` and `g(x)=-x^2+x-1`

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Thus, quotient = `x-2` and remainder = `3`

Quotient * Divisor + Remainder

`= (x - 2) * (-x^2 + x - 1) + 3`

`= -x^3 + x^2 - x + 2x^2 - 2x + 2 + 3`

`= -x^3 + 3x^2 - 3x + 5`

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