Question:
By actual division, find the quotient and the remainder when the first
polynomial is divided by the second polynomial x4 + 1 and x-1.
Solution:
Using long division method,
$x-1) x^{4}+1\left(x^{3}+x^{2}+x+1\right.$
$\frac{x^{4}-x^{3}}{x^{3}+1}$
$\frac{x^{3}-x^{2}}{x^{2}+1}$
$\frac{x^{2}-x}{x+1}$
Hence, Quotient $=x^{3}+x^{2}+x+1$ and Remainder $=2$
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