Question
Divide the first polynomial by the second polynomial in the following. Also write the quotient and remainder:
$\frac{\text{x}^4-\text{x}^3+5\text{x}}{\text{x}-1}$

Answer

$\frac{\text{x}^4-\text{x}^3+5\text{x}}{\text{x}-1}$
$=\frac{\text{x}^3(\text{x}-1)+5(\text{x}-1)+5}{\text{x}-1}$
$=\frac{(\text{x}^3+5)(\text{x}-1)+5}{\text{x}-1}$
$=\Big(\text{x}^3+5\Big)+\frac{5}{\text{x}-1}$
Therefore, quotient $=x^3+5$ and remainder = 5

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