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Division of a Polynomial by a Monomial

The quotient ...

Question

The quotient obtained when $x^{4} + x^{3} - 2 x^{2} + x - 1$ is divided by $x - 1$ is

x^{3} + 2 x^{2} - 1

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x^{3} + 2 x^{2} + 1

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x^{3} - 2 x^{2} + 1

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x^{3} - 2 x^{2} - 1

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Solution

The correct option is B $x^{3} + 2 x^{2} + 1$
The required division is shown below:
Hence, the quotient obtained when $x^{4} + x^{3} - 2 x^{2} + x - 1$ is divided by $x - 1$ is $x^{3} + 2 x^{2} + 1$ .

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When $x^{4} + x^{3} - 2 x^{2} + x + 1$ is divided by x-1, the remainder is 2 and the quotient is q(x). Find q(x).

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