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

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Solution

Using long division method,

Quotient = $x^{3} + x^{2} + x + 1$ and Remainder = 2

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x^{4} + 1

Question 13
By actual division, find the quotient and the remainder when the first polynomial $x^{4} + 1$ is divided by the polynomial (x - 1)

x^{4} + 1

x - 1

(x^{4} - 2 x^{3} + 2 x^{2} + x + 4)

(x^{2} + x + 1)

By actual division, find the quotient and the remainder when $(x^{4} + 1)$ is divided by (x - 1).
Verify that remainder = f(1).

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