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Question
By actual division, find the quotient and the remainder when the first polynomial is divided by the second polynomial: x4 + 1; x – 1
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Solution
Using long division method,
`x - 1")"overline(x^4 + 1)(x^3 + x^2 + x + 1`
x4 – x3
– +
x3 + 1
x3 – x2
– +
x2 + 1
x2 – x
– +
x + 1
x – 1
– +
2
Hence, from the above long division method, we get,
Quotient = x3 + x2 + x + 1
Remainder = 2.
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