By actual division, find the quotient and the remainder when the first polynomial is divided by the second polynomial : $x^{4} + 1; x - 1$

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

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

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x^{3} + x^{2} + x + 1, 5

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

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Solution

The correct option is D $x^{3} + x^{2} + x + 1, 2$
Here, First polynomial $x^{4} + 1$
Second Polynomial $x - 1$

Quotient : $x^{3} + x^{2} + x + 1$
Remainder : $2$

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x^{4} + x^{3} - 2 x^{2} + x + 1

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